scholarly journals Comb Model with Non-Static Stochastic Resetting and Anomalous Diffusion

2020 ◽  
Vol 4 (2) ◽  
pp. 28 ◽  
Author(s):  
Maike Antonio Faustino dos Santos

Nowadays, the stochastic resetting process is an attractive research topic in stochastic process. At the same time, a series of researches on stochastic diffusion in complex structures introduced ways to understand the anomalous diffusion in complex systems. In this work, we propose a non-static stochastic resetting model in the context of comb structure that consists of a structure formed by backbone in x axis and branches in y axis. Then, we find the exact analytical solutions for marginal distribution concerning x and y axis. Moreover, we show the time evolution behavior to mean square displacements (MSD) in both directions. As a consequence, the model revels that until the system reaches the equilibrium, i.e., constant MSD, there is a Brownian diffusion in y direction, i.e., ⟨ ( Δ y ) 2 ⟩ ∝ t , and a crossover between sub and ballistic diffusion behaviors in x direction, i.e., ⟨ ( Δ x ) 2 ⟩ ∝ t 1 2 and ⟨ ( Δ x ) 2 ⟩ ∝ t 2 respectively. For static stochastic resetting, the ballistic regime vanishes. Also, we consider the idealized model according to the memory kernels to investigate the exponential and tempered power-law memory kernels effects on diffusive behaviors. In this way, we expose a rich class of anomalous diffusion process with crossovers among them. The proposal and the techniques applied in this work are useful to describe random walkers with non-static stochastic resetting on comb structure.

2021 ◽  
Vol 148 ◽  
pp. 111009
Author(s):  
Zhaoyang Wang ◽  
Ping Lin ◽  
Erhui Wang

2015 ◽  
Vol 19 (4) ◽  
pp. 1177-1181
Author(s):  
Yan-Mei Qin ◽  
Hua Kong ◽  
Kai-Teng Wu ◽  
Xiao-Ming Zhu

Fractional calculus can always exactly describe anomalous diffusion. Recently the discrete fractional difference is becoming popular due to the depiction of non-linear evolution on discrete time domains. This paper proposes a diffusion model with two terms of discrete fractional order. The numerical simulation is given to reveal various diffusion behaviors.


Author(s):  
Lin Liu ◽  
Shuo Yang ◽  
Libo Feng ◽  
Qian Xu ◽  
Liancun Zheng ◽  
...  

This paper considers a novel distributed order time fractional dual-phase-lag model to analyze the anomalous diffusion in a comb structure, which has a widespread application in medicine and biology. The newly proposed constitution model is a generalization of the dual-phase-lag model, in which a spectrum of the time fractional derivatives with the memory characteristic governed by the weight coefficient is considered and the formulated governing equation contains both the diffusion and wave characteristics. With the L1-formula to discrete the time Caputo fractional derivatives, the finite difference method is used to discretize the model and the related numerical results are plotted graphically. By adding a source term, an exact solution is defined to verify the correctness of the numerical scheme and the convergence order of the error in spatial direction is presented. Finally, the dynamic characteristics of the particle distributions and the effects of involved parameters on the total number of particles in the [Formula: see text]-direction are analyzed in detail.


2020 ◽  
Author(s):  
Shawn Yoshida ◽  
William Schmid ◽  
Nam Vo ◽  
William Calabrase ◽  
Lydia Kisley

AbstractAnomalous diffusion dynamics in confined nanoenvironments govern the macroscale properties and interactions of many biophysical and material systems. Currently, it is difficult to quantitatively link the nanoscale structure of porous media to anomalous diffusion within them. Fluorescence correlation spectroscopy super-resolution optical fluctuation imaging (fcsSOFI) has been shown to extract nanoscale structure and Brownian diffusion dynamics within gels, liquid crystals, and polymers, but has limitations which hinder its wider application to more diverse, biophysically-relevant datasets. Here, we parallelize the least-squares curve fitting step on a GPU improving computation times by up to a factor of 40, implement anomalous diffusion and two-component Brownian diffusion models, and make fcsSOFI more accessible by packaging it in a user-friendly GUI. We apply fcsSOFI to simulations of the protein fibrinogen diffusing in polyacrylamide of varying matrix densities and super-resolve locations where slower, anomalous diffusion occurs within smaller, confined pores. The improvements to fcsSOFI in speed, scope, and usability will allow for the wider adoption of super-resolution correlation analysis to diverse research topics.


2020 ◽  
pp. 153-153
Author(s):  
Zhaoyang Wang ◽  
Liancun Zheng ◽  
Lianxi Ma ◽  
Goong Chen

A kind of anomalous diffusion and heat transfer on a comb structure with anisotropic relaxation are studied, which can be used to model many problems in Biologic and Nature in fractal porous media. The Hausdorff derivative is introduced and new governing equations is formulated in view of fractal dimension. Numerical solutions are obtained and the Fox H-function analytical solutions is given for special cases. The particles spatial-temporal evolution(STE)and the mean square displacement(MSD)versus time are presented. The effects of back bone and finger relaxation parameters, and the time fractal parameter are discussed. Results show that the MSD decreases with the increase of back bone parameter or the decrease of finger relaxation parameter in a short of time, but they have little effect on MSD in a long period. Particularly, the MSD has time dependence in the form of t?/2 (0 < ? ? 1)when t>?, which indicates that the diffusion is an anomalous sub-diffusion and heat transfer.


Toxins ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 343 ◽  
Author(s):  
Bastian Bräuning ◽  
Michael Groll

Recent technological advances have seen increasing numbers of complex structures from diverse pore-forming toxins (PFT). The ClyA family of α-PFTs comprises a broad variety of assemblies including single-, two- and three-component toxin systems. With crystal structures available for soluble subunits of all major groups in this extended protein family, efforts now focus on obtaining molecular insights into physiological pore formation. This review provides an up-to-date discussion on common and divergent structural and functional traits that distinguish the various ClyA family PFTs. Open questions of this research topic are outlined and discussed.


Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 221
Author(s):  
Trifce Sandev ◽  
Viktor Domazetoski ◽  
Alexander Iomin ◽  
Ljupco Kocarev

This review addresses issues of various drift–diffusion and inhomogeneous advection problems with and without resetting on comblike structures. Both a Brownian diffusion search with drift and an inhomogeneous advection search on the comb structures are analyzed. The analytical results are verified by numerical simulations in terms of coupled Langevin equations for the comb structure. The subordination approach is one of the main technical methods used here, and we demonstrated how it can be effective in the study of various random search problems with and without resetting.


Nanophotonics ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Seungkyun Park ◽  
Ikbeom Lee ◽  
Jungmin Kim ◽  
Namkyoo Park ◽  
Sunkyu Yu

Abstract The independent tailoring of wave quantities lays the foundation for controlling wave phenomena and designing wave devices. The concept of isospectrality, which suggests the existence of systems that provide identical spectra, has inspired a novel route to the spectrum-preserved engineering of wave–matter interactions in photonics, acoustics, and quantum mechanics. Recently, in photonics, constructing isospectral optical structures has become an emerging research topic to handle the intricate spectral responses of the systems composed of many-particles or inhomogeneous materials. The cornerstones in this field have stimulated the realization of non-Hermitian systems with real eigenspectra, one-dimensional structures exhibiting higher-dimensional physics, and novel engineering methodologies for broadband devices such as phase-matched multiplexers and multimodal lasing platforms. Here we review recent achievements based on isospectrality in photonics. We outline milestones in two different subfields of supersymmetric photonics and interdimensional isospectrality. We illustrate that isospectrality has paved the way for the independent control of wave quantities, showing great potential for the analytical and platform-transparent design of photonic systems with complex structures and materials.


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