[show abstract][hide abstract] ABSTRACT: In fluorescence fluctuation polarization sensitive experiments, the limitations associated with detecting the rotational timescale are usually eliminated by applying fluorescence correlation spectroscopy analysis. In this paper, the variance of the time-averaged fluorescence intensity extracted from the second moment of the measured fluorescence intensity is analyzed in the short time limit, before fluctuations resulting from rotational diffusion average out. Since rotational correlation times of fluorescence molecules are typically much lower than the temporal resolution of the system, independently of the time bins used, averaging over an ensemble of time-averaged trajectories was performed in order to construct the time-averaged intensity distribution, thus improving the signal-to-noise ratio. Rotational correlation times of fluorescein molecules in different viscosities of the medium within the range of the anti-bunching time (1-10 ns) were then extracted using this method.
[show abstract][hide abstract] ABSTRACT: A general framework to include fluctuations in the single molecule
fluorescence intensity (FI) signal due to random changes in molecule
dipole orientation was introduced at Optics Express (21, 2007). By
assuming continuous changes in dipole orientation described by Brownian
rotational diffusion, this research derives the probability density
function (PDF) equation of FI fluctuations. Solution of the proposed
equation for several limiting cases and different correlation times
yields the short time behavior of FI fluctuations. Monte Carlo
simulations results, in accordance with those found in theory will be
presented during our talk.
[show abstract][hide abstract] ABSTRACT: We obtain an equation for the distribution of functionals of the path of a particle undergoing sub-diffusive continuous-time random-walk. Our equation is a fractional generalization of the Feynman-Kac equation for Brownian functionals and makes use of the substantial fractional derivative operator introduced by Friedrich and co-workers. We also derive a backward equation that depends on the initial position rather than the final one, and equations for a process with underlying Levy flights. As applications, we derive the PDFs of the occupation time in half-space, the first passage time, and the maximum of the walk; and calculate the average residence time in an interval, the survival probability if the interval is absorbing, and the moments of the area under the random walk curve. Comment: 24 pages, 4 figures
[show abstract][hide abstract] ABSTRACT: Functionals of Brownian motion have diverse applications in physics, mathematics, and other fields. The probability density
function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, which is a Schrödinger equation in imaginary time.
In recent years there is a growing interest in particular functionals of non-Brownian motion, or anomalous diffusion, but
no equation existed for their PDF. Here, we derive a fractional generalization of the Feynman-Kac equation for functionals of anomalous paths based on sub-diffusive continuous-time random
walk. We also derive a backward equation and a generalization to Lévy flights. Solutions are presented for a wide number of
applications including the occupation time in half space and in an interval, the first passage time, the maximal displacement,
and the hitting probability. We briefly discuss other fractional Schrödinger equations that recently appeared in the literature.
KeywordsContinuous-time random-walk-Anomalous diffusion-Feynman-Kac equation-Levy flights-Fractional calculus
Journal of Statistical Physics 01/2010; 141(6):1071-1092. · 1.40 Impact Factor
[show abstract][hide abstract] ABSTRACT: We derive backward and forward fractional Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing anomalous diffusion. Fractional substantial derivatives introduced by Friedrich and co-workers [Phys. Rev. Lett. 96, 230601 (2006)10.1103/PhysRevLett.96.230601] provide the correct fractional framework for the problem. For applications, we calculate the distribution of occupation times in half space and show how the statistics of anomalous functionals is related to weak ergodicity breaking.