195 research outputs found
Monte Carlo evaluation of FADE approach to anomalous kinetics
In this paper we propose a comparison between the CTRW (Monte Carlo) and
Fractional Derivative approaches to the modelling of anomalous diffusion
phenomena in the presence of an advection field. Galilei variant and invariant
schemes are revised.Comment: 13 pages, 6 figure
Bayesian Inversion with Neural Operator (BINO) for Modeling Subdiffusion: Forward and Inverse Problems
Fractional diffusion equations have been an effective tool for modeling
anomalous diffusion in complicated systems. However, traditional numerical
methods require expensive computation cost and storage resources because of the
memory effect brought by the convolution integral of time fractional
derivative. We propose a Bayesian Inversion with Neural Operator (BINO) to
overcome the difficulty in traditional methods as follows. We employ a deep
operator network to learn the solution operators for the fractional diffusion
equations, allowing us to swiftly and precisely solve a forward problem for
given inputs (including fractional order, diffusion coefficient, source terms,
etc.). In addition, we integrate the deep operator network with a Bayesian
inversion method for modelling a problem by subdiffusion process and solving
inverse subdiffusion problems, which reduces the time costs (without suffering
from overwhelm storage resources) significantly. A large number of numerical
experiments demonstrate that the operator learning method proposed in this work
can efficiently solve the forward problems and Bayesian inverse problems of the
subdiffusion equation
Rocking Subdiffusive Ratchets: Origin, Optimization and Efficiency
We study origin, parameter optimization, and thermodynamic efficiency of
isothermal rocking ratchets based on fractional subdiffusion within a
generalized non-Markovian Langevin equation approach. A corresponding
multi-dimensional Markovian embedding dynamics is realized using a set of
auxiliary Brownian particles elastically coupled to the central Brownian
particle (see video on the journal web site). We show that anomalous
subdiffusive transport emerges due to an interplay of nonlinear response and
viscoelastic effects for fractional Brownian motion in periodic potentials with
broken space-inversion symmetry and driven by a time-periodic field. The
anomalous transport becomes optimal for a subthreshold driving when the driving
period matches a characteristic time scale of interwell transitions. It can
also be optimized by varying temperature, amplitude of periodic potential and
driving strength. The useful work done against a load shows a parabolic
dependence on the load strength. It grows sublinearly with time and the
corresponding thermodynamic efficiency decays algebraically in time because the
energy supplied by the driving field scales with time linearly. However, it
compares well with the efficiency of normal diffusion rocking ratchets on an
appreciably long time scale
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