25 papers · ranked by Valyu relevance
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…
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…
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…
Tadeusz Kosztołowicz, Aldona Dutkiewicz, Katarzyna D. Lewandowska
The ordinary subdiffusion equation, with fractional time derivatives of at most first order, describes a process in which the propagation velocity of diffusing molecules is unlimited. To avoid this non-physical property the Cattaneo diffusion equation has been proposed. Compared to the ordinary subdiffusion equation…
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…
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, 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…
Vivek Tyagi, Alan T. Ly, Gabriella A. Bertaccini, Elizabeth L. Evans + 3 more
The mechanically-activated ion channel Piezo1 is involved in numerous physiological processes. Piezo1 is activated by diverse mechanical cues and is gated by membrane tension. The channel has been found to be mobile in the plasma membrane. We employed single particle tracking (SPT) of endogenously-expressed…
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…
A. Barletta
The analysis of the Rayleigh-B´enard instability due to the mass diffusion in a fluid-saturated horizontal porous layer is reconsidered. The standard diffusion theory based on the variance of the molecular position growing linearly in time is generalised to anomalous diffusion, where the variance is modelled as a…
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…
Eugene B. Postnikov, Anastasia I. Lavrova, Dmitry E. Postnov, Cecília R. Santos + 2 more
'Cecília R. Santos' 'Telma Quintela' 'Isabel Goncalves'] The mechanisms of transport of substances in the brain parenchyma have been a hot topic in scientific discussion in the past decade. This discussion was triggered by the proposed glymphatic hypothesis, which assumes a directed flow of cerebral fluid within the…
Grzegorz Pawlik, Antoni C. Mitus, Alberto Gutiérrez
Upconversion (UC) luminescence in doped lanthanide nanocrystals is associated with the energy migration (EM) process within clusters of dopant ions. The process of the synthesis of core-shell nanocrystals occurs at elevated temperatures, promoting the diffusion of the dopants into the shell accompanied by the decay of…
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…
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…
Arsalan Rahimabadi, Habib Benali
In a variety of practical applications, there is a need to investigate diffusion or reaction-diffusion processes on complex structures, including brain networks, that can be modeled as weighted undirected and directed graphs. As an instance, the celebrated Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP)…
Gabriel Barreiro, Vladimir Pérez-Veloz
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local models. This paper investigates a nonlinear diffusion equation where the…
François Simon, Guillaume Ramadier, Inès Fonquernie, Janka Zsok + 5 more
Single-particle tracking is a powerful tool for understanding protein dynamics and characterizing microenvironments. As the motion of unconstrained nanoscale particles is governed by Brownian diffusion, deviations from this behavior are biophysically insightful. However, the stochastic nature of particle movement and…
Conrad Möckel, Abin Biswas, Simone Reber, Aleksei Chechkin + 2 more
Understanding of the dynamics inherent to biological matter is crucial for illuminating the physical mechanisms underlying cellular processes. In this study, we employ bright-field differential dynamic microscopy (DDM) to investigate density fluctuations inherent in a cell-free model of eukaryotic cytoplasm. Our…
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…
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…
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…