共查询到20条相似文献,搜索用时 62 毫秒
1.
Michael E. Hough 《Celestial Mechanics and Dynamical Astronomy》1989,47(1):57-85
A reversible dynamical system with two degrees-of-freedom is reduced to a second-order, Hamiltonian system under a change of independent variable. In certain circumstances, the reduced order system may be integrated following an orthogonal curvilinear transformation from Cartesian x,y to intrinsic orbital coordinates , . Solutions for the orbit position and true time variables are expressed by: % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiabg2 % da9iaadAgacaGGOaGaeqOVdGNaaiilaiabeE7aOjaacMcacaGGSaGa % aeiiaiaadMhacqGH9aqpcaWGNbGaaiikaiabe67a4jaacYcacqaH3o % aAcaGGPaGaaiilaiaabccacaWGKbGaamiDaiabg2da9iabgglaXoaa % dmaabaWaaSaaaeaacaWGibWaa0baaKqaahaacqaH+oaEaeaacaqGYa % aaaOGaam4raiabgUcaRiaadIeadaqhaaqcbaCaaiabeE7aObqaaiaa % ikdaaaGccaWGfbaabaGaaGOmaiaacIcacaWGibGaey4kaSIaamyvai % aacMcaaaaacaGLBbGaayzxaaWaaWbaaSqabKqaGhaacaaIXaGaai4l % aiaaikdaaaGccaWGKbGaeqiXdqhaaa!6498! \[ x = f(\xi ,\eta ),{\rm{ }}y = g(\xi ,\eta ),{\rm{ }}dt = \pm \left[ {\frac{{_\xi ^{\rm{2}} {\ie} + _\eta ^2 }}{{2( + U)}}} \righ \]1446 1040 where U is the potential function, and z is the new independent variable. The functions f, g may be expressed by quadratures when the metric coefficients {\er},{\ie} are specified. Two second-order, partial differential equations specify {\er}, {\ie} and Hamiltonian {\tH}. Auxiliary conditions are needed because the solutions are underdetermined. For example, both sets of curvilinear coordinate lines are orbits when certain dynamical compatibility conditions between U and {\ie} (or {\er}) are satisfied. Alternatively, when orbits cross the parametric curves, the auxiliary condition {\er} = {\ie} specifies a conformal transformation, and the partial differential equation for {\tH} may be reduced to an ordinary differential equation for the orbit curve. In either case, integrability is guaranteed for Lionville dynamical systems. Specific applications are presented to illustrate direct solution for the orbit (e.g., two fixed centers) and inverse solution for the potential. 相似文献
2.
L. K. Babadzanjanz 《Celestial Mechanics and Dynamical Astronomy》1979,20(1):43-57
The method of obtaining the estimates of the maximalt-interval (
–,
+) on which the solution of theN-body problem exists and which is such that some fixed mutual distance (e. g.
12) exceeds some fixed non-negative lower bound, for allt contained in (
–,
+), is considered. For given masses and initial data, the increasing sequences of the numbers
k
, each of which provides the estimate
+ >
k
, are constructed. It appears that if
+ = +, then
. 相似文献
3.
It is generally believed that the only known reaction in whichC
p
violation definitely occurs is in the decay of the long-lived neutralK-mesonK
L
+–,K
L
00, andK
L
e
±±
v (Christensonet al., 1964: Sivaram, 1982). No attempt has been made to studyC
p
violation outside theK-system for quite a long time. Recently,C
p
violation effects have been reported in the hyperon decays through the reaction
(Bassompierre, 1990) with asymmetry at the level of 10–3 to 10–4.In this paper we examine the possible implications of hyperon decays asymmetry in some cosmic-ray sources. We identify cosmic-ray sources where such decays can occur. The signatures for measuring these asymmetries in both the laboratory and cosmic-ray sources are examined.It is found that there is a correlation between these signatures. We conclude that hyperon decays contribute significantly toC
p
violation observed in cosmic-ray sources. 相似文献
4.
Makhlouf Amar 《Celestial Mechanics and Dynamical Astronomy》1991,52(4):397-406
We consider the Hill's equation: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca% WGKbWaaWbaaSqabeaacaaIYaaaaOGaeqOVdGhabaGaamizaiaadsha% daahaaWcbeqaaiaaikdaaaaaaOGaey4kaSYaaSaaaeaacaWGTbGaai% ikaiaad2gacqGHRaWkcaaIXaGaaiykaaqaaiaaikdaaaGaam4qamaa% CaaaleqabaGaaGOmaaaakiaacIcacaWG0bGaaiykaiabe67a4jabg2% da9iaaicdaaaa!4973!\[\frac{{d^2 \xi }}{{dt^2 }} + \frac{{m(m + 1)}}{2}C^2 (t)\xi = 0\]Where C(t) = Cn (t, {frbuilt|1/2}) is the elliptic function of Jacobi and m a given real number. It is a particular case of theame equation. By the change of variable from t to defined by: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaqcaawaaOWaaiqaaq% aabeqaamaalaaajaaybaGaamizaGGaaiab-z6agbqaaiaadsgacaWG% 0baaaiabg2da9OWaaOaaaKaaGfaacaGGOaqcKbaG-laaigdajaaycq% GHsislkmaaleaajeaybaGaaGymaaqaaiaaikdaaaqcaaMaaeiiaiaa% bohacaqGPbGaaeOBaOWaaWbaaKqaGfqabaGaaeOmaaaajaaycqWFMo% GrcqWFPaqkaKqaGfqaaaqcaawaaiab-z6agjab-HcaOiab-bdaWiab% -LcaPiab-1da9iab-bdaWaaakiaawUhaaaaa!51F5!\[\left\{ \begin{array}{l}\frac{{d\Phi }}{{dt}} = \sqrt {(1 - {\textstyle{1 \over 2}}{\rm{ sin}}^{\rm{2}} \Phi )} \\\Phi (0) = 0 \\\end{array} \right.\]it is transformed to the Ince equation: (1 + · cos(2)) y + b · sin(2) · y + (c + d · cos(2)) y = 0 where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaqcaawaaiaadggacq% GH9aqpcqGHsislcaWGIbGaeyypa0JcdaWcgaqaaiaaigdaaeaacaaI% ZaGaaiilaiaabccacaWGJbGaeyypa0Jaamizaiabg2da9aaacaqGGa% WaaSaaaKaaGfaacaWGTbGaaiikaiaad2gacqGHRaWkcaaIXaGaaiyk% aaqaaiaaiodaaaaaaa!4777!\[a = - b = {1 \mathord{\left/{\vphantom {1 {3,{\rm{ }}c = d = }}} \right.\kern-\nulldelimiterspace} {3,{\rm{ }}c = d = }}{\rm{ }}\frac{{m(m + 1)}}{3}\]In the neighbourhood of the poles, we give the expression of the solutions.The periodic solutions of the Equation (1) correspond to the periodic solutions of the Equation (3). Magnus and Winkler give us a theory of their existence. By comparing these results to those of our study in the case of the Hill's equation, we can find the development in Fourier series of periodic solutions in function of the variable and deduce the development of solutions of (1) in function of C(t). 相似文献
5.
P. M. Papaelias 《Earth, Moon, and Planets》1987,38(1):13-20
A general velocity-height relation for both antimatter and ordinary matter meteor is derived. This relation can be expressed as % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq% aHfpqDdaWgaaWcbaGaamOEaaqabaaakeaacqaHfpqDdaWgaaWcbaGa% eyOhIukabeaaaaGccqGH9aqpcaqGLbGaaeiEaiaabchacaqGGaWaam% WaaeaacqGHsisldaWcaaqaaiaadkeaaeaacaWGHbaaaiaabwgacaqG% 4bGaaeiCaiaabIcacaqGTaGaamyyaiaadQhacaGGPaaacaGLBbGaay% zxaaGaeyOeI0YaaSaaaeaacaWGdbaabaGaamOqaiabew8a1naaBaaa% leaacqGHEisPaeqaaaaakmaacmaabaGaaGymaiabgkHiTiaabwgaca% qG4bGaaeiCamaadmaabaGaeyOeI0YaaSaaaeaacaWGcbaabaGaamyy% aaaacaqGLbGaaeiEaiaabchacaqGOaGaaeylaiaadggacaWG6bGaai% ykaaGaay5waiaaw2faaaGaay5Eaiaaw2haaiaacYcaaaa!64FD!\[\frac{{\upsilon _z }}{{\upsilon _\infty }} = {\text{exp }}\left[ { - \frac{B}{a}{\text{exp( - }}az)} \right] - \frac{C}{{B\upsilon _\infty }}\left\{ {1 - {\text{exp}}\left[ { - \frac{B}{a}{\text{exp( - }}az)} \right]} \right\},\]where
z
is the velocity of the meteoroid at height z, its velocity before entrance into the Earth's atmosphere, is the scale-height, and C parameter proportional to the atom-antiatom annihilation cross- section, which is experimentally unknown. The parameter B (B = DA0/m) is the well known parameter for koinomatter (ordinary matter) meteors, D is the drag factor, 0 is the air density at sea level, A is the cross sectional area of the meteoroid and m its mass.When the annihilation cross-section is zero — in the case of ordinary meteors — the parameter C is also zero and the above derived equation becomes % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq% aHfpqDdaWgaaWcbaGaamOEaaqabaaakeaacqaHfpqDdaWgaaWcbaGa% eyOhIukabeaaaaGccqGH9aqpcaqGLbGaaeiEaiaabchacaqGGaWaam% WaaeaacqGHsisldaWcaaqaaiaadkeaaeaacaWGHbaaaiaabwgacaqG% 4bGaaeiCaiaabIcacaqGTaGaamyyaiaadQhacaGGPaaacaGLBbGaay% zxaaGaaiilaaaa!4CF5!\[\frac{{\upsilon _z }}{{\upsilon _\infty }} = {\text{exp }}\left[ { - \frac{B}{a}{\text{exp( - }}az)} \right],\]which is the well known velocity-height relation for koinomatter meteors.In the case in which the Universe contains antimatter in compact solid structure, the velocity-height relation can be found useful.Work performed mainly at the Nuclear Physics Laboratory of the National University of Athens, Greece. 相似文献
6.
We define a stretching number (or Lyapunov characteristic number for one period) (or stretching number) a = In % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaqWaaeaada% Wcaaqaaiabe67a4jaadshacqGHRaWkcaaIXaaabaGaeqOVdGNaamiD% aaaaaiaawEa7caGLiWoaaaa!3F1E!\[\left| {\frac{{\xi t + 1}}{{\xi t}}} \right|\]as the logarithm of the ratio of deviations from a given orbit at times t and t + 1. Similarly we define a helicity angle as the angle between the deviation % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOVdGNaam% iDaaaa!3793!\[\xi t\]and a fixed direction. The distributions of the stretching numbers and helicity angles (spectra) are invariant with respect to initial conditions in a connected chaotic domain. We study such spectra in conservative and dissipative mappings of 2 degrees of freedom and in conservative mappings of 3-degrees of freedom. In 2-D conservative systems we found that the lines of constant stretching number have a fractal form. 相似文献
7.
Klaus Becker 《Celestial Mechanics and Dynamical Astronomy》1974,9(2):269-289
Zusammenfassung Es wird gezeigt, daß die unter der Einwirkung einer Momentenimpulsserie entstehende Bewegung eines rotierenden Flugkörpers mit Nutationsdämpfung sich vollständig einem regelmäßigen Polygon entnehmen läßt, das durch das Trägheitsmomentenverhältnis, den Integralwert eines Einzelimpulses, den Drall und eine die Dämpfung charakterisierende KonstanteK
0 bestimmt ist.Die Bewegung setzt sich aus logarithmischen Spiralen zusammen, derenn-ten Anfangsradius man erhält, indem man den Teilungspunkt des im VerhältnisK
0:1 geteilten (n–1)-ten Radius mit der (n+1)-ten Polygonecke verbindet.Es wird bewiesen, daß das Konstruktionsnetz zu einem im äußeren Polygon liegenden ähnlichen inneren Polygon konvergiert, das gegenüber ersterem gedreht ist.Einfache Beziehungen zur Bewegungsbestimmung mit dem Polygonschema werden für Pulsfrequenzen angegeben, die ganzzahlige Vielfache oder Bruchteile der Spinfrequenz sind.
Symbole 1-2-3 Achsen des flugkörperfesten Koordinatensystems - a,b,c Hilfsgrößen zur Bestimmung der Iterationsgrößen - E i i-te Polygonecke - H Drall des Flugkörpers - K i Verhältnis deri-ten Drehzeigerlängen zu Beginn und am Ende eines Impulses - M Iterationsmatrix - Integralwert des Momentenimpulses - P 0 Äußeres Polygon - P 1 Spitze des Drehzeigersr 00e - P Drehpunkt des Drehzeigersr 00 - P Konvergierendes Polygon - P i Teilungspunkt des [i–1]-ten Zeigers - r 0i Drehzeiger aufgrund desi-ten Impulses allein - r 0ia Zeigerr 0i in Anfangslage - r 0ie Zeigerr 0i in Endlage - r i i-ter Summenzeiger - r ia Zeigerr i in Anfangslage - r ie Zeigerr i in Endlage - T Dauer einer Flugkörperumdrehung - t,t, Zeitargumente - x-y-z Achsen eines raumfesten Koordinatensystems - x i ,y i Iterationskoordinaten - n Phase desn-ten Radius gegenüber der anliegenden Polygonseite - Drehung des inneren Polygons gegenüber dem äußeren - Abklingkonstante - Phasenänderung des Drehzeigers innerhalb einer Flugkörperumdrehung - 0 Anteil der über 2 hinausgehenden Phasenänderung des Drehzeigers - 3 Trägheitsmoment um die Spinachse - 12 Trägheitsmoment um die Querachsen - Zahl der Ecken des Konstruktionspolygons - 1,2 Eigenwerte der Iterationsmatrix - Zahl der vollen Umläufe des Konstruktionspolygons - Fortbewegungsachse des Drallvektors - 0 Ausgangsphasenwinkel - i Phasenlage desi-ten Summenzeigers - x, y Drehwinkel nach Einzelimpuls fürt - , Funktionen der Iterationsgrößen - , Drehwinkel umx-bzw.y-Achse - Drehgeschwindigkeit der Spinachse um den Drallvektor - Fiktive Größen bei Pulsfrequenzen kleiner als Spinfrequenz - Fiktive Größen bei Pulsfrequenzen größer als Spinfrequenz 相似文献
It is shown that the motion of a spinning body with nutation damping due to a series of torque pulses can be completely derived from a regular polygon determined by the ratio of inertias, the integral of one pulse, the momentum and a constantK 0 characterizing damping.The motion is composed of spirals thenth initial radius of which is obtained by connecting the dividing point of the (n–1)th radius with the (n+1)th polygon corner. Each dividing point divides the respective radius in the ratioK 0:1. The net of construction lines converges into an inner polygon turned against the outer one and having the same shape.Simple rules are shown for the application of the scheme on pulse frequencies which are multiples or fractions of spin frequency.
Symbole 1-2-3 Achsen des flugkörperfesten Koordinatensystems - a,b,c Hilfsgrößen zur Bestimmung der Iterationsgrößen - E i i-te Polygonecke - H Drall des Flugkörpers - K i Verhältnis deri-ten Drehzeigerlängen zu Beginn und am Ende eines Impulses - M Iterationsmatrix - Integralwert des Momentenimpulses - P 0 Äußeres Polygon - P 1 Spitze des Drehzeigersr 00e - P Drehpunkt des Drehzeigersr 00 - P Konvergierendes Polygon - P i Teilungspunkt des [i–1]-ten Zeigers - r 0i Drehzeiger aufgrund desi-ten Impulses allein - r 0ia Zeigerr 0i in Anfangslage - r 0ie Zeigerr 0i in Endlage - r i i-ter Summenzeiger - r ia Zeigerr i in Anfangslage - r ie Zeigerr i in Endlage - T Dauer einer Flugkörperumdrehung - t,t, Zeitargumente - x-y-z Achsen eines raumfesten Koordinatensystems - x i ,y i Iterationskoordinaten - n Phase desn-ten Radius gegenüber der anliegenden Polygonseite - Drehung des inneren Polygons gegenüber dem äußeren - Abklingkonstante - Phasenänderung des Drehzeigers innerhalb einer Flugkörperumdrehung - 0 Anteil der über 2 hinausgehenden Phasenänderung des Drehzeigers - 3 Trägheitsmoment um die Spinachse - 12 Trägheitsmoment um die Querachsen - Zahl der Ecken des Konstruktionspolygons - 1,2 Eigenwerte der Iterationsmatrix - Zahl der vollen Umläufe des Konstruktionspolygons - Fortbewegungsachse des Drallvektors - 0 Ausgangsphasenwinkel - i Phasenlage desi-ten Summenzeigers - x, y Drehwinkel nach Einzelimpuls fürt - , Funktionen der Iterationsgrößen - , Drehwinkel umx-bzw.y-Achse - Drehgeschwindigkeit der Spinachse um den Drallvektor - Fiktive Größen bei Pulsfrequenzen kleiner als Spinfrequenz - Fiktive Größen bei Pulsfrequenzen größer als Spinfrequenz 相似文献
8.
Multiple expansion of the tidal potential 总被引:1,自引:0,他引:1
F. Mignard 《Celestial Mechanics and Dynamical Astronomy》1978,18(3):287-294
The Earth tidal deformation causes an additional gravitational potential. Its effect on the Moon orbital motion has been studied by several authors.In this contribution, we develop this additional potential without specifying the inertial frame chosen.For this purpose, we use the properties of the representation of rotation groups in 3 dimensions space. We finally obtain the interaction potential between the distorted Earth and the Moon which is a necessary preliminary to the study of the evolution of the Earth-Moon system.Nomenclature T.R.O
Tide raising object
- (, , )
Spherical coordinates of the T.R.O.
- (J,
E
)
Earth spin axis orientation.
E
is the longitude of the ascending node of Earth's equator on thexy-plane
- (a
,I
,e
, , ,M
)
Elliptics elements of the T.R.O 相似文献
9.
Shuichi Tamazawa Kiyotaka Toyama Noboru Kaneko Yôrô Ôno 《Astrophysics and Space Science》1975,32(2):403-421
Spherically symmetric, steady-state, optically thick accretion onto a nonrotating black hole with the mass of
is studied. The gas accreting onto the black hole is assumed to be a fully ionized hydrogen plasma withn
0=108 cm–3 andT
0=104 K far from the black hole, and a new approximate expression for the Eddington factor is introduced. The luminosity is estimated to beL=1.875×1033 erg s–1, which primarily arises from the optical surface (1) ofT104 K. The accretion flow is characterized by 1 and (v/c)10. In the optically thin region, the flow remains isothermal, and the increase of temperature occurs at 1. The radiative equilibrium is strictly realized at (v/c)10. 相似文献
10.
The light curved in the CM field 总被引:1,自引:0,他引:1
In this paper we introduce the CM field in Sections 2 and 3 based on the paper by Wang and Peng (1985), and calculate the light curved in the CM field in Section 4. The result shows thatP makes CM larger than C at
, and smaller at
. Under a special circumstance which source, CM lens, and observer are in the same line, if we get |
0=0
,
and |
=/2
, we can determine theP(M) andQ(M) of the CM lens,M is the mass of the CM lens. 相似文献
11.
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 相似文献
12.
In our preceding paper {see [L. Sh. Grigorian and S. Gottlöber, Astrofizika (in press)]} we investigated a self-gravitating system consisting of a scalar field and a linear tensor field ik= ki with minimal coupling and with allowance for the action of vacuum polarization effects. In the present paper we investigate the case of a nonlinear tensor field ik. The action S
()
of the field ik is determined by the difference Rik — ik, where Rik is the space-time Ricci tensor and Rik is the analogous quantity constructed using the metric ik=gik+ik induced by ik ( is a free parameter). Here
S
()
coincides with the previously known expression for the action of a linear field ik. Equations of motion are derived for ik in curved space-time. The energy-momentum metric tensor, determining the contribution of ik to the gravitational field equations, is calculated.Translated from Astrofizika, Vol. 39, No. 1, pp. 135–144, January-March, 1996. 相似文献
13.
Computations of polarization and intensity of radiation from a unit stellar surface area are presented, as well as a study of the numerical characteristics of atmospheres — single-scattering albedo and the initial source function(), which define the polarization behaviour of atmospheres. The radiatively stable models of stellar atmospheres presented by Kuruczet al. (1974) and Kurucz (1979) have been used for calculations. Since the versus optical depth dependence is rather weak, it has been assumed that (=cost. With a fixed effective temperatureT
eff maximum values of are characteristic of stars featuring the lowest surface gravity accelerationg. Among stars with radiatively stable atmospheres, maximum values of (=5000 Å) 0.4–0.6 are exhibited by supergiants withT
eff=8000–20 000 K. The plot of () is characterized by discontinuities at the boundaries of spectral series for hydrogen and, sometimes, for helium. Maximum are attained in the Lyman region of =912–1200 Å, where can reach the value 0.7–0.9 for supergiants, this value being 0.3 for Main-Sequence stars. For stars withT
eff 35 000 K, high values of also are attained for <912 Å. Within the infrared region, is always small because of bremsstrahlung absorption.A rapid growth of the source functionB
with < typical for ultraviolet range (within the Wien part of spectrum), together with high values of results in the strong polarization of emission from a unit stellar surface element, sometimes exceeding the values for the case of a pure electron scattering. For longer wavelengths, where the limb-darkening coefficient is smaller, the plane of polarization abruptly turns 90° in the central parts of the visible stellar disk. 相似文献
14.
I. H. Urch 《Astrophysics and Space Science》1984,104(2):357-366
The diffusion of charged particles in a stochastic magnetic field (strengthB) which is superimposed on a uniform magnetic fieldB
0
k is studied. A slab model of the stochastic magnetic field is used. Many particles were released into different realizations of the magnetic field and their subsequent displacements z in the direction of the uniform magnetic field numerically computed. The particle trajectories were calculated over periods of many particle scattering times. The ensemble average
was then used to find the parallel diffusion coefficient
. The simulations were performed for several types of stochastic magnetic fields and for a wide range of particle gyro-radius and the parameterB/B
0. The calculations have shown that the theory of charged particle diffusion is a good approximation even when the stochastic magnetic field is of the same strength as the uniform magnetic field. 相似文献
15.
In this paper we consider the low-frequency limit of the electromagnetic and gravitational radiation from a relativistic particle falling into a Kerr black hole. The radiation spectra are obtained with help of the solution of Teukolsky's equations in terms of the hypergeometric functions. It is shown that in the low-frequency limit the spectra are flat and the power radiated depends strongly on the radiation spin. Dependence of the power on the initial kinetic energy of the radiating particle has the same character as that obtained by the WKB technique for the band of frequencies
, where 0=(1–u
0
2
/c
2)–1/2 is the particle Lorentz factor at infinity. The full energy radiated is proportional to 0 in 0 for electromagnetic radiation and to
0
3
for gravitational radiation. 相似文献
16.
A. M. I. Osman 《Astrophysics and Space Science》1985,116(2):299-311
Surface photometry of the UV continuum galaxy NGC 838 has been carried out in theB, V system using photographic plates obtained with the 74 Kottamia telescope, Egypt. Isophotes, luminosity profiles, integrated photographic magnitudes, effective diameters and other photometric parameters are derived.The photoelectrically calibrated total apparent magnitudes areB
T
=13.57 with maximum diameters 1.57×1.34 (at threshold
m
=27.7 mag.//) andV
T
=12.91 with maximum diameters 1.54×1.32 (at threshold
m
=27.7 mag./). The integrated colour index(B–V)
T
=0.66 and the effective surface brightness
e
(B=19.0 mag./) and
e
(V=19.7 mag./. The major axis is at position angle =85°±1°.The nucleus of NGC 838 is quite blue (integrated colour(B–V)=0.41 forr
*<0.1) compared to normal galaxies while the colour becomes redder from the nucleus outwards. The UV excess, H emission and radio continuum emission previously observed from this galaxy by other investigators may be attributed to a recent burst of star formation in the nucleus of the galaxy of duration slightly greater than 2×107 yr. 相似文献
17.
Boris Garfinkel 《Celestial Mechanics and Dynamical Astronomy》1983,30(4):373-383
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 mj(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
. 相似文献
18.
T. P. Singh A. K. Agrawal H. L. Agrawal A. Raptis 《Astrophysics and Space Science》1991,181(2):171-181
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, Jy, Jz)
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 相似文献
19.
Since there are reasons for expecting supersymmetry in an underlying quantum theory of gravity, one is led to study quantum and classical cosmology with supergravity. In particular, classical solutions corresponding to these models could also be used to generate the quantization of supersymmetric minisuperspaces. In generating these solutions, the solution to the Rarita-Schwinger field in the cosmological background is also obtained. In this paper the supercosmological equations of Einstein-Rarita-Schwinger are solved for the micro-superspace sector of the Taub model, under the assumption =11*22 and
. The solution for the parameters of the metric and are proportional to each other in each order, the zeroth-order and also the second-order terms. The zeroth-order terms correspond to the solution in general relativity and are logarithmic in time, the 12 terms have an hyperbolic time-dependence. The Rarita-Schwinger field has the form cos((2/D
3)ln |t–t
0|) and oscillates an infinite number of times astt
0. This oscillating behaviour of the solution for is not only present when spinor fields are treated in a curved background, but also some cosmological wave functions behave in this manner. This solution is at the same time the supercosmological solution for the microsuperspace sector of the Taub model and also the Rarita-Schwinger field in this background.This work was supported in part by CONACYT grant P228CCOX891723, and DGICSA SEP grant C90-03-0347. 相似文献
20.
By considering the relativistic expression for isothermal NS cores,T·e
/2 = constant, we have shown that some of the standard equations of state, when applied to NS cores, correspond to constancy of some adiabatic exponents. It has been shown that the equation of state,P=KE, corresponds to 1 = to 2 = 3 1 +K and the equation of state, dP/dE=K, corresponds to 3 1 +K. The conditions under which different equations of state represent isothermal cores have been obtained: For isothermal NS, the local temperatureT, can be expressed in terms of pressureP, energy densityE, and rest mass density . For example: (a)P =KE
:T = constant × (E/); (b)P=KE :T = constant × (P/); (c) dP/dE =K :T
K
; (d) = 2 :T = constant × (P/E); and (e) = 3 :T = constant × (P/)1/2. Equation of state corresponding to = 2 is obtained as:P=E/ln(K/E) and the equation corresponding to = 3 comes out as:E=P ln(K/P). Core-envelope models can be developed for these two cases. When core equation corresponding to = 2 or = 3 is used in the core, we can ensure the continuity of dP/dE at the core-envelope boundary, along with the continuity ofP, E, , and . The parameters of isothermal NS cores corresponding to the cases = 2 and = 3, have been obtained. The maximum mass of these NS cores comes out to be 2.7 . 相似文献