A new collection of real world applications of fractional calculus in science and engineering
Fractional calculus is at this stage an arena where many models are still to be introduced,
discussed and applied to real world applications in many branches of science and …
discussed and applied to real world applications in many branches of science and …
Multiscale simulations of biological membranes: the challenge to understand biological phenomena in a living substance
Biological membranes are tricky to investigate. They are complex in terms of molecular
composition and structure, functional over a wide range of time scales, and characterized by …
composition and structure, functional over a wide range of time scales, and characterized by …
Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities
A growing number of biological, soft, and active matter systems are observed to exhibit
normal diffusive dynamics with a linear growth of the mean-squared displacement, yet with a …
normal diffusive dynamics with a linear growth of the mean-squared displacement, yet with a …
Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking
Modern microscopic techniques following the stochastic motion of labelled tracer particles
have uncovered significant deviations from the laws of Brownian motion in a variety of …
have uncovered significant deviations from the laws of Brownian motion in a variety of …
Protein crowding in lipid bilayers gives rise to non-Gaussian anomalous lateral diffusion of phospholipids and proteins
Biomembranes are exceptionally crowded with proteins with typical protein-to-lipid ratios
being around 1∶ 50− 1∶ 100. Protein crowding has a decisive role in lateral membrane …
being around 1∶ 50− 1∶ 100. Protein crowding has a decisive role in lateral membrane …
Manipulation and motion of organelles and single molecules in living cells
K Norregaard, R Metzler, CM Ritter… - Chemical …, 2017 - ACS Publications
The biomolecule is among the most important building blocks of biological systems, and a
full understanding of its function forms the scaffold for describing the mechanisms of higher …
full understanding of its function forms the scaffold for describing the mechanisms of higher …
Tempered fractional calculus
F Sabzikar, MM Meerschaert, J Chen - Journal of Computational Physics, 2015 - Elsevier
Fractional derivatives and integrals are convolutions with a power law. Multiplying by an
exponential factor leads to tempered fractional derivatives and integrals. Tempered …
exponential factor leads to tempered fractional derivatives and integrals. Tempered …
[HTML][HTML] Non-Brownian diffusion in lipid membranes: Experiments and simulations
The dynamics of constituents and the surface response of cellular membranes—also in
connection to the binding of various particles and macromolecules to the membrane—are …
connection to the binding of various particles and macromolecules to the membrane—are …
Biological membrane organization and cellular signaling
To execute their many vital functions, cell membranes are highly organized. Here, we review
how membrane structure shapes signal transduction across membranes. Recent …
how membrane structure shapes signal transduction across membranes. Recent …
Anomalous diffusion, aging, and nonergodicity of scaled Brownian motion with fractional Gaussian noise: Overview of related experimental observations and models
How does a systematic time-dependence of the diffusion coefficient D (t) affect the ergodic
and statistical characteristics of fractional Brownian motion (FBM)? Here, we answer this …
and statistical characteristics of fractional Brownian motion (FBM)? Here, we answer this …