25 papers · ranked by Valyu relevance
Tadeusz Kosztołowicz, Aldona Dutkiewicz, Katarzyna D. Lewandowska
The ordinary subdiffusion equation, with a fractional time derivative of at most first order, describes a process in which the propagation velocity of diffusing molecules is unlimited. To avoid this non-physical property different forms of the Cattaneo subdiffusion equation have been proposed. We define the Cattaneo…
Toby Kay, Luca Giuggioli
We derive, through subordination techniques, a generalized Feynman-Kac equation in the form of a time fractional Schrödinger equation. We relate such equation to a functional which we name the subordinated local time. We demonstrate through a stochastic treatment how this generalized Feynman-Kac equation describes…
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…
Tadeusz Kosztołowicz, Aldona Dutkiewicz
A g–subdiffusion equation with fractional Caputo time derivative with respect to another function g is used to describe a process of a continuous transition from subdiffusion with parameters α and Dα to subdiffusion with parameters β and Dβ. The parameters are defined by the time evolution of the mean square…
Tadeusz Kosztołowicz, Aldona Dutkiewicz, Katarzyna D. Lewandowska, Sławomir Wa̧sik + 1 more
'Sławomir Wa̧sik' 'Michał Arabski'] Anomalous diffusion of antibiotic (colistin) in a system consisting of packed gel (alginate) beads immersed in water is studied experimentally and theoretically. The experimental studies are performed using the interferometric method of measuring concentration profiles of diffusing…
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, Katarzyna D. Lewandowska
We have proposed a new stochastic interpretation of the sudiffusion described by the Sharma–Mittal entropy formalism which generates a nonlinear subdiffusion equation with natural order derivatives. We have shown that the solution to the diffusion equation generated by Gauss entropy (which is the particular case of…
Tadeusz Kosztołowicz, Katarzyna D. Lewandowska
We consider the subdiffusion–reaction process with reactions of a type A + B −→ B (in which particles A are assumed to be mobile whereas B — static) in comparison to the subdiffusion– reaction process with A −→ B reactions which was studied by I.M. Sokolov, M.G.W. Schmidt, and F. Sagu´es in Phys. Rev. E 73, 031102…
Fernando Diaz-Diaz, Ernesto Estrada
Normal and anomalous diffusion are ubiquitous in many complex systems [1]. Here, we define a time and space generalized diffusion equation (GDE), which uses fractional-time derivatives and transformed d-path Laplacian operators on graphs/networks. We find analytically the solution of this equation and prove that it…
Konstantin Speckner, Florian Rehfeldt, Matthias Weiss
The interior of cellular nuclei, the nucleoplasm, is a crowded fluid that is pervaded by protein-decorated DNA polymers, the chromatin. Due to the complex architecture of chromatin and a multitude of associated non-equilbrium processes, e.g. DNA repair, the nucleoplasm can be expected to feature non-trivial material…
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…
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…
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…
Tadeusz Kosztołowicz, Ralf Metzler, Sławomir Wa̧sik, Michał Arabski
We study theoretically and empirically ciprofioxacin antibiotic diffusion through a gel-like artificial sputum medium (ASM) mimicking physiological conditions typical for a cystic fibrosis layer, in which regions occupied by Pseudomonas aeruginosa bacteria are present. Our theoretical model is based on the…
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…
Marco Palombo, Andrea Barbetta, Cesare Cametti, Gabriele Favero + 2 more
'Silvia Capuani' 'Georgios Bokias'] Considering the current development of new nanostructured and complex materials and gels, it is critical to develop a sub-micro-scale sensitivity tool to quantify experimentally new parameters describing sub-microstructured porous systems. Diffusion NMR, based on the measurement of…
Alberto Sapora, Marco Codegone, G. Barbero
We discuss the diffusion phenomenon in the parabolic and hyperbolic regimes. New effects related to the finite velocity of the diffusion process are predicted, that can partially explain the strange behavior associated to adsorption phenomenon. For sake of simplicity, the analysis is performed by considering a sample…
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…
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…
Nils Edvin Richard Zimmermann, Gabriela Guevara-Carrion, Jadran Vrabec, Niels Hansen
The thermodiffusion behavior of binary Lennard-Jones mixtures in the liquid state was investigated by combining the individual strengths of non-equilibrium molecular dynamics (NEMD) and equilibrium molecular dynamics (EMD) simulations. On the one hand, boundarydriven NEMD simulations are useful to quickly predict Soret…
Sarthak Patnaik
We know that the diffusion is defined as the movement of molecules under a potential gradient. It is characterized by the diffusion coefficient. Diffusion coefficient determination can be done via various techniques, but in this paper, we have had a broad look at interferometry based optical methods for diffusion…
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…