1,899 research outputs found
Steady shocks around black holes produced by sub-keplerian flows with negative energy
We discuss a special case of formation of axisymmetric shocks in the
accretion flow of ideal gas onto a Schwarzschild black hole: when the total
energy of the flow is negative. The result of our analysis enlarges the
parameter space for which these steady shocks are exhibited in the accretion of
gas rotating around relativistic stellar objects. Since keplerian disks have
negative total energy, we guess that, in this energy range, the production of
the shock phenomenon might be easier than in the case of positive energy. So
our outcome reinforces the view that sub-keplerian flows of matter may
significantly affect the physics of the high energy radiation emission from
black hole candidates. We give a simple procedure to obtain analytically the
position of the shocks. The comparison of the analytical results with the data
of 1D and 2D axisymmetric numerical simulations confirms that the shocks form
and are stable.Comment: 5 pages, 5 figures, accepted by MNRAS on 10 November 200
Primes and prime ideals in short intervals
We prove the analog of Cram\'er's short intervals theorem for primes in
arithmetic progressions and prime ideals, under the relevant Riemann
Hypothesis. Both results are uniform in the data of the underlying structure.
Our approach is based mainly on the inertia property of the counting functions
of primes and prime ideals.Comment: minor change to Proposition
Simulation of Thick Accretion Disks with Standing Shocks by Smoothed Particle Hydrodynamics
We present results of numerical simulation of inviscid thick accretion disks
and wind flows around black holes. We use Smoothed Particle Hydrodynamics (SPH)
technique for this purpose. Formation of thick disks are found to be preceded
by shock waves travelling away from the centrifugal barrier. For a large range
of the parameter space, the travelling shock settles at a distance close to the
location obtained by a one-and-a-half dimensional model of inviscid accretion
disks. Occasionally, it is observed that accretion processes are aided by the
formation of oblique shock waves, particularly in the initial transient phase.
The post-shock region (where infall velocity suddenly becomes very small)
resembles that of the usual model of thick accretion disk discussed in the
literature, though they have considerable turbulence. The flow subsequently
becomes supersonic before falling into the black hole. In a large number of
cases which we simulate, we find the formation of strong winds which are hot
and subsonic when originated from the disk surface very close to the black hole
but become supersonic within a few tens of the Schwarzschild radius of the
blackhole. In the case of accretion of high angular momentum flow, very little
amount of matter is accreted directly onto the black hole. Most of the matter
is, however, first squeezed to a small volume close to the black hole, and
subsequently expands and is expelled as a strong wind. It is quite possible
that this expulsion of matter and the formation of cosmic radio jets is aided
by the shock heating in the inner parts of the accretion disks.Comment: LaTeX, 16 pages, Astrophysical Journal (in press
In-plane structure and ordering at liquid sodium surfaces and interfaces from ab initio molecular dynamics
Atoms at liquid metal surfaces are known to form layers parallel to the
surface. We analyze the two-dimensional arrangement of atoms within such layers
at the surface of liquid sodium, using ab initio molecular dynamics (MD)
simulations based on density functional theory. Nearest neighbor distributions
at the surface indicate mostly 5-fold coordination, though there are noticeable
fractions of 4-fold and 6-fold coordinated atoms. Bond angle distributions
suggest a movement toward the angles corresponding to a six-fold coordinated
hexagonal arrangement of the atoms as the temperature is decreased towards the
solidification point. We rationalize these results with a distorted hexagonal
order at the surface, showing a mixture of regions of five and six-fold
coordination. The liquid surface results are compared with classical MD
simulations of the liquid surface, with similar effects appearing, and with ab
initio MD simulations for a model solid-liquid interface, where a pronounced
shift towards hexagonal ordering is observed as the temperature is lowered
Explicit bounds for generators of the class group
Assuming Generalized Riemann's Hypothesis, Bach proved that the class group SICK of a number field K may be generated using prime ideals whose norm is bounded by 121og(2)delta(K), and by (4 + o(l)) log(2) delta(K) asymptotically, where delta(K) is the absolute value of the discriminant of K. Under the same assumption, Belabas, Diaz y Diaz and Friedman showed a way to determine a set of prime ideals that generates SICK and which performs better than Bach's bound in computations, but which is asymptotically worse. In this paper we show that SICK is generated by prime ideals whose norm is bounded by the minimum of 4.01 log(2) delta(K), 4(l + (2 pi e(gamma))N-_(K))(2) log(2) delta(k) and 4( log delta(k) + log log delta(K) - (gamma + log 2 pi)N-K + 1 + (N-K + 1) log(7log delta(K)/log delta(K))(2). Moreover, we prove explicit upper bounds for the size of the set determined by Belabas, Diaz y Diaz and Friedma's algorithms, confirming that it has size SIC (log delta(K) log log delta(K))(2). In addition, we propose a different algorithm which produces a set of generators which satisfies the above mentioned bounds and in explicit computations turns out to be smaller than log(2) delta(K) except for 7 out of the 31292 fields we tested
Stable nitrile oxide dipolar cycloadditions in pure water
A systematic study on the behaviour of stable 2,4,6-trimethyl-3,5-dichlorobenzonitrile oxide versus a number of mono-, bi- and trisubstituted dipolarophiles in water was pursued obtaining simple as well as annulated isoxazolines. Reaction conditions changed with the dipolarophilic species, according to their solubility in water and the degree of substitution of the reactive carbon\u2013carbon multiple bond. The presence of sodium dodecylsulfate was also tested as potential micellar catalyst
Small values of signed harmonic sums
For every \u3c4 08R and every integer N, let mN(\u3c4) be the minimum of the distance of \u3c4 from the sums 11n=1Nsn/n, where s1,\u2026,sn 08 121,+1. We prove that mN(\u3c4
3D SPH Simulations of Shocks in Accretion Flows around black holes
We present the simulation of 3D time dependent flow of rotating ideal gas
falling into a Schwarzschild black hole. It is shown that also in the 3D case
steady shocks are formed in a wide range of parameters (initial angular
momentum and thermal energy). We therefore highlight the stability of the
phenomenon of shock formation in sub keplerian flows onto black holes, and
reenforce the role of the shocks in the high luminosity emission from black
hole candidates. The simulations have been performed using a parallelized code
based on the Smoothed Particles Hydrodynamics method (SPH). We also discuss
some properties of the shock problem that allow its use as a quantitative test
of the accuracy of the used numerical method. This shows that the accuracy of
SPH is acceptable although not excellent.Comment: 9 pages, 22 figure
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