19 papers · ranked by Valyu relevance
Tadeusz Kosztołowicz, Mohammad Reza Rahimi Tabar
Superdiffusion is usually defined as a random walk process of a molecule, in which the time evolution of the mean-squared displacement, $σ2$, of the molecule is a power function of time, $σ2(t)∼t(2/γ)$, with $γ\in(1,2)$. An equation with a Riesz-type fractional derivative of the order $γ$ with respect to a spatial…
Tadeusz Kosztołowicz, Aldona Dutkiewicz, Katarzyna D. Lewandowska
Normal and anomalous diffusion processes are characterized by the time evolution of the mean square displacement of a diffusing molecule $σ2(t)$. When $σ2(t)$ is a power function of time, the process is described by a fractional subdiffusion, fractional superdiffusion or normal diffusion equation. However, for other…
Tadeusz Kosztołowicz
We use a subdiffusion equation with fractional Caputo time derivative with respect to another function g (g–subdiffusion equation) to describe a smooth transition from ordinary subdiffusion to superdiffusion. Ordinary subdiffusion is described by the equation with the "ordinary" fractional Caputo time derivative…
Tadeusz Kosztołowicz, Aldona Dutkiewicz
Recently, in the paper: T. Koszto lowicz and A. Dutkiewicz, Phys. Rev. E 104, 014118 (2021) the g–subdiffusion equation with fractional Caputo time derivative with respect to another function g has been considered. This equation offers new possibilities for modelling diffusion such as a process in which a type of…
Tadeusz Kosztołowicz, Aldona Dutkiewicz
We show an application of a subdiffusion equation with Caputo fractional time derivative with respect to another function g to describe subdiffusion in a medium having a structure evolving over time. In this case a continuous transition from subdiffusion to other type of diffusion may occur. The process can be…
Tadeusz Kosztołowicz
Subdiffusion equation and molecule survival equation, both with Caputo fractional time derivatives with respect to another functions g1 and g2, respectively, are used to describe diffusion of a molecule that can disappear at any time with a constant probability. The process can be interpreted as "ordinary" subdiffusion…
Jakub Spiechowicz, Jerzy Łuczka
We reveal the mechanism of subdiffusion which emerges in a straightforward, one dimensional classical nonequilibrium dynamics of a Brownian ratchet driven by both a time-periodic force and Gaussian white noise. In a tailored parameter set for which the deterministic counterpart is in a non-chaotic regime, subdiffusion…
Gerd Baumann, Robert F Place, Zeno Földes-Papp
In living cell or its nucleus, the motions of molecules are complicated due to the large crowding and expected heterogeneity of the intracellular environment. Randomness in cellular systems can be either spatial (anomalous) or temporal (heterogeneous). In order to separate both processes, we introduce anomalous random…
Jialiang Wei, Jie Lin
While the regulation of bacterial cell size is widely studied across generations, the stochastic nature of cell volume growth remains elusive within a cell cycle. Here, we investigate the fluctuations of cell volume growth and report a deviation from standard white-noise models: the random growth rate exhibits…
Anna S. Bodrova, Aleksei V. Chechkin, Andrey G. Cherstvy, Hadiseh Safdari + 2 more
'Hadiseh Safdari' 'Igor M. Sokolov' 'Ralf Metzler'] It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an…
Ernesto Estrada
The COVID-19 respiratory disease is caused by the novel coronavirus SARS-CoV-2, which uses the enzyme ACE2 to entry human cells. This disease is characterized by important damages at multi-organ level, partially due to the abundant expression of ACE2 in practically all human tissues. However, not every organ in which…
M. J. Saxton
Single-particle tracking experiments have measured the distribution of escape times of DNA-binding species diffusing in living cells: CRISPR-Cas9, TetR, and LacI. The observed distribution is a truncated power law. One important property of this distribution is that it is inconsistent with a Gaussian distribution of…
Antonio Cobarrubia, Jarod Tall, Austin Crispin-Smith, Antoni Luque
Mucus is a fluid that protects animals against pathogens while promoting interactions with commensal microbes. Changes in the diffusivity of particles in mucus alter viruses’ infectivity, the efficiency of bacterial pathogens to invade a host, and the effectivity of drug delivery. Multiple physicochemical properties…
Kolja Klett, Andrey G. Cherstvy, Jaeoh Shin, Igor M. Sokolov + 1 more
We employ Langevin-dynamics simulations to unveil non-Brownian and non-Gaussian center-of-mass self-diffusion of massive flexible dumbbell-shaped particles in crowded two-dimensional solutions. We also study the intra-dumbbell dynamics due to the relative motion of the two constituent elastically-coupled disks. Our…
Aishani Ghosal, Yu-Huan Wang, Nguyen Nguyen, Laura Troyer + 1 more
Advances in fluorescence microscopy have enabled high-resolution tracking of individual biomolecules in living cells. However, accurate estimation of diffusion parameters from single-particle trajectories remains challenging due to static and dynamic localization errors inherent in these measurements. While previous…
Aleksei V. Chechkin, Igor M. Sokolov
Generalized (non-Markovian) diffusion equations with different memory kernels and subordination schemes based on random time change in the Brownian diffusion process are popular mathematical tools for description of a variety of non-Fickian diffusion processes in physics, biology and earth sciences. Some of such…
Jixin Chen
Predicting the reaction kinetics, that is, how fast a reaction can happen in a solution, is essential information for many processes, such as industrial chemical manufacturing, refining, synthesis and separation of petroleum products, environmental processes in air and water, biological reactions in cells, biosensing…
Yu-Chuan Chien, Haidong Liu, Ashok S. Menon, William R. Brant + 2 more
The galvanostatic intermittent titration technique (GITT) has been regarded as the go-to method for determining the diffusion coefficients of Li-ions in insertion electrode materials at various states of charge (SoC). However, the method is time-consuming. In this work, the intermittent current interruption (ICI)…
Jixin Chen
Predicting the reaction kinetics, that is, how fast a reaction can happen in a solution, is essential information for many processes, such as industrial chemical manufacturing, refining, synthesis and separation of petroleum products, environmental processes in air and water, biological reactions in cells, biosensing…