7,383 research outputs found
Importance Sampling for Multiscale Diffusions
We construct importance sampling schemes for stochastic differential
equations with small noise and fast oscillating coefficients. Standard Monte
Carlo methods perform poorly for these problems in the small noise limit. With
multiscale processes there are additional complications, and indeed the
straightforward adaptation of methods for standard small noise diffusions will
not produce efficient schemes. Using the subsolution approach we construct
schemes and identify conditions under which the schemes will be asymptotically
optimal. Examples and simulation results are provided
Methanol as a tracer of fundamental constants
The methanol molecule CH3OH has a complex microwave spectrum with a large
number of very strong lines. This spectrum includes purely rotational
transitions as well as transitions with contributions of the internal degree of
freedom associated with the hindered rotation of the OH group. The latter takes
place due to the tunneling of hydrogen through the potential barriers between
three equivalent potential minima. Such transitions are highly sensitive to
changes in the electron-to-proton mass ratio, mu = m_e/m_p, and have different
responses to mu-variations. The highest sensitivity is found for the mixed
rotation-tunneling transitions at low frequencies. Observing methanol lines
provides more stringent limits on the hypothetical variation of mu than ammonia
observation with the same velocity resolution. We show that the best quality
radio astronomical data on methanol maser lines constrain the variability of mu
in the Milky Way at the level of |Delta mu/mu| < 28x10^{-9} (1sigma) which is
in line with the previously obtained ammonia result, |Delta mu/mu| < 29x10^{-9}
(1\sigma). This estimate can be further improved if the rest frequencies of the
CH3OH microwave lines will be measured more accurately.Comment: 7 pages, 1 table, 1 figure. Accepted for publication in Ap
Calculation of spectral distribution of X-radiation absorbed in the earth's atmosphere
Calculation of spectral distribution of X ray energy absorbed in earth atmospher
Biodiversity, extinctions and evolution of ecosystems with shared resources
We investigate the formation of stable ecological networks where many species
share the same resource. We show that such stable ecosystem naturally occurs as
a result of extinctions. We obtain an analytical relation for the number of
coexisting species and find a relation describing how many species that may go
extinct as a result of a sharp environmental change. We introduce a special
parameter that is a combination of species traits and resource characteristics
used in the model formulation. This parameter describes the pressure on system
to converge, by extinctions. When that stress parameter is large we obtain that
the species traits concentrate at some values. This stress parameter is thereby
a parameter that determines the level of final biodiversity of the system.
Moreover, we show that dynamics of this limit system can be described by simple
differential equations
Sensitivity of the H3O+ inversion-rotational spectrum to changes in m_e/m_p
Quantum mechanical tunneling inversion transition in ammonia NH3 is actively
used as a sensitive tool to study possible variations of the electron-to-proton
mass ratio, mu = m_e/m_p. The molecule H3O+ has the inversion barrier
significantly lower than that of NH3. Consequently, its tunneling transition
occurs in the far-infrared (FIR) region and mixes with rotational transitions.
Several such FIR and submillimiter transitions are observed from the
interstellar medium in the Milky Way and in nearby galaxies. We show that the
rest-frame frequencies of these transitions are very sensitive to the variation
of mu, and that their sensitivity coefficients have different signs. Thus, H3O+
can be used as an independent target to test hypothetical changes in mu
measured at different ambient conditions of high (terrestrial) and low
(interstellar medium) matter densities. The environmental dependence of mu and
coupling constants is suggested in a class of chameleon-type scalar field
models - candidates to dark energy carrier.Comment: 8 pages, 2 figures, accepted to ApJ; v2: reformatted for ApJ and
discussion of systematics significantly extende
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