63,479 research outputs found

### Mechanism of Magnetic Flux Loss in Molecular Clouds

We investigate the detailed processes working in the drift of magnetic fields
in molecular clouds. To the frictional force, whereby the magnetic force is
transmitted to neutral molecules, ions contribute more than half only at cloud
densities $n_{\rm H} < 10^4 {\rm cm}^{-3}$, and charged grains contribute more
than 90% at $n_{\rm H} > 10^6 {\rm cm}^{-3}$. Thus grains play a decisive role
in the process of magnetic flux loss. Approximating the flux loss time $t_B$ by
a power law $t_B \propto B^{-\gamma}$, where $B$ is the mean field strength in
the cloud, we find $\gamma \approx 2$, characteristic to ambipolar diffusion,
only at $n_{\rm H} < 10^7 {\rm cm}^{-3}$. At higher densities, $\gamma$
decreases steeply with $n_{\rm H}$, and finally at $n_{\rm H} \approx n_{\rm
dec} \approx {\rm a few} \times 10^{11} {\rm cm}^{-3}$, where magnetic fields
effectively decouple from the gas, $\gamma << 1$ is attained, reminiscent of
Ohmic dissipation, though flux loss occurs about 10 times faster than by Ohmic
dissipation. Ohmic dissipation is dominant only at $n_{\rm H} > 1 \times
10^{12} {\rm cm}^{-3}$. While ions and electrons drift in the direction of
magnetic force at all densities, grains of opposite charges drift in opposite
directions at high densities, where grains are major contributors to the
frictional force. Although magnetic flux loss occurs significantly faster than
by Ohmic dissipation even at very high densities as $n_{\rm H} \approx n_{\rm
dec}$, the process going on at high densities is quite different from ambipolar
diffusion in which particles of opposite charges are supposed to drift as one
unit.Comment: 34 pages including 9 postscript figures, LaTex, accepted by
Astrophysical Journal (vol.573, No.1, July 1, 2002

### Quasi-Monte Carlo methods for Choquet integrals

We propose numerical integration methods for Choquet integrals where the
capacities are given by distortion functions of an underlying probability
measure. It relies on the explicit representation of the integrals for step
functions and can be seen as quasi-Monte Carlo methods in this framework. We
give bounds on the approximation errors in terms of the modulus of continuity
of the integrand and the star discrepancy.Comment: 6 page

### Inverse stochastic optimal controls

We study an inverse problem of the stochastic optimal control of general
diffusions with performance index having the quadratic penalty term of the
control process. Under mild conditions on the drift, the volatility, the cost
functions of the state, and under the assumption that the optimal control
belongs to the interior of the control set, we show that our inverse problem is
well-posed using a stochastic maximum principle. Then, with the well-posedness,
we reduce the inverse problem to some root finding problem of the expectation
of a random variable involved with the value function, which has a unique
solution. Based on this result, we propose a numerical method for our inverse
problem by replacing the expectation above with arithmetic mean of observed
optimal control processes and the corresponding state processes. The recent
progress of numerical analyses of Hamilton-Jacobi-Bellman equations enables the
proposed method to be implementable for multi-dimensional cases. In particular,
with the help of the kernel-based collocation method for
Hamilton-Jacobi-Bellman equations, our method for the inverse problems still
works well even when an explicit form of the value function is unavailable.
Several numerical experiments show that the numerical method recover the
unknown weight parameter with high accuracy

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