4,933 research outputs found
Asymptotic expansions and fast computation of oscillatory Hilbert transforms
In this paper, we study the asymptotics and fast computation of the one-sided
oscillatory Hilbert transforms of the form where the bar indicates the Cauchy principal value and is a
real-valued function with analytic continuation in the first quadrant, except
possibly a branch point of algebraic type at the origin. When , the
integral is interpreted as a Hadamard finite-part integral, provided it is
divergent. Asymptotic expansions in inverse powers of are derived for
each fixed , which clarify the large behavior of this
transform. We then present efficient and affordable approaches for numerical
evaluation of such oscillatory transforms. Depending on the position of , we
classify our discussion into three regimes, namely, or
, and . Numerical experiments show that the convergence
of the proposed methods greatly improve when the frequency increases.
Some extensions to oscillatory Hilbert transforms with Bessel oscillators are
briefly discussed as well.Comment: 32 pages, 6 figures, 4 table
First-Passage Time Distribution and Non-Markovian Diffusion Dynamics of Protein Folding
We study the kinetics of protein folding via statistical energy landscape
theory. We concentrate on the local-connectivity case, where the
configurational changes can only occur among neighboring states, with the
folding progress described in terms of an order parameter given by the fraction
of native conformations. The non-Markovian diffusion dynamics is analyzed in
detail and an expression for the mean first-passage time (MFPT) from non-native
unfolded states to native folded state is obtained. It was found that the MFPT
has a V-shaped dependence on the temperature. We also find that the MFPT is
shortened as one increases the gap between the energy of the native and average
non-native folded states relative to the fluctuations of the energy landscape.
The second- and higher-order moments are studied to infer the first-passage
time (FPT) distribution. At high temperature, the distribution becomes close to
a Poisson distribution, while at low temperatures the distribution becomes a
L\'evy-like distribution with power-law tails, indicating a non-self-averaging
intermittent behavior of folding dynamics. We note the likely relevance of this
result to single-molecule dynamics experiments, where a power law (L\'evy)
distribution of the relaxation time of the underlined protein energy landscape
is observed.Comment: 26 pages, 10 figure
Self organized criticality in an improved Olami-Feder-Christensen model
An improved version of the Olami-Feder-Christensen model has been introduced
to consider avalanche size differences. Our model well demonstrates the
power-law behavior and finite size scaling of avalanche size distribution in
any range of the adding parameter of the model. The probability
density functions (PDFs) for the avalanche size differences at consecutive time
steps (defined as returns) appear to be well approached, in the thermodynamic
limit, by q-Gaussian shape with appropriate q values which can be obtained a
priori from the avalanche size exponent . For the small system sizes,
however, return distributions are found to be consistent with the crossover
formulas proposed recently in Tsallis and Tirnakli, J. Phys.: Conf. Ser. 201,
012001 (2010). Our results strengthen recent findings of Caruso et al. [Phys.
Rev. E 75, 055101(R) (2007)] on the real earthquake data which support the
hypothesis that knowing the magnitude of previous earthquakes does not make the
magnitude of the next earthquake predictable. Moreover, the scaling relation of
the waiting time distribution of the model has also been found.Comment: 16 pages, 6 figure
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