Brownian motion of N interacting particles. II. Hydrodynamical evaluation of the diffusion tensor matrix

1973 ◽  
Vol 59 (4) ◽  
pp. 1833-1840 ◽  
Author(s):  
J. L. Aguirre ◽  
T. J. Murphy
Keyword(s):  
Brownian Motion ◽  
Diffusion Tensor ◽  
Interacting Particles

A perfect probe: Resonance of underdamped scaled Brownian motion

2021 ◽  
Author(s):  
Yuhui Luo ◽  
Chunhua Zeng ◽  
Baowen Li
Keyword(s):  
Brownian Motion ◽  
Single Particle ◽  
Brownian Particle ◽  
Bistable System ◽  
Velocity Autocorrelation Function ◽  
Interacting Particles ◽  
Velocity Autocorrelation ◽  
Spectrum Density ◽  
Coupling Strengths ◽  
And Diffusion

Abstract We numerically investigate the resonance of the underdamped scaled Brownian motion in a bistable system for both cases of a single particle and interacting particles. Through the velocity autocorrelation function (VACF) and mean squared displacement (MSD) of a single particle, we find that for the steady state, diffusions are ballistic at short times and then become normal for most of parameter regimes. However, for certain parameter regimes, both VACF and MSD suggest that the transition between superdiffusion and subdiffusion takes place at intermediate times, and diffusion becomes normal at long times. Via the power spectrum density corresponding to the transitions, we find that there exists a nontrivial resonance. For interacting particles, we find that the interaction between the probe particle and other particles can lead to the resonance, too. Thus we theoretically propose the system with the Brownian particle as a probe, which can detect the temperature of the system and identify the number of the particles or the types of different coupling strengths in the system. The probe is potentially useful for detecting microscopic and nanometer-scale particles and for identifying cancer cells or healthy ones.

scholarly journals In Silico Neuro-Oncology: Brownian Motion-Based Mathematical Treatment as a Potential Platform for Modeling the Infiltration of Glioma Cells into Normal Brain Tissue

2015 ◽  
Vol 14s4 ◽  
pp. CIN.S19341 ◽  
Author(s):  
Markos Antonopoulos ◽  
Georgios Stamatakos
Keyword(s):  
Brownian Motion ◽  
Brain Tissue ◽  
Diffusion Tensor ◽  
Glioma Cells ◽  
Tomographic Imaging ◽  
Mathematical Treatment ◽  
Normal Brain ◽  
Imaging Data ◽  
Clinical Observations ◽  
Anisotropic Character

Intensive glioma tumor infiltration into the surrounding normal brain tissues is one of the most critical causes of glioma treatment failure. To quantitatively understand and mathematically simulate this phenomenon, several diffusion-based mathematical models have appeared in the literature. The majority of them ignore the anisotropic character of diffusion of glioma cells since availability of pertinent truly exploitable tomographic imaging data is limited. Aiming at enriching the anisotropy-enhanced glioma model weaponry so as to increase the potential of exploiting available tomographic imaging data, we propose a Brownian motion-based mathematical analysis that could serve as the basis for a simulation model estimating the infiltration of glioblastoma cells into the surrounding brain tissue. The analysis is based on clinical observations and exploits diffusion tensor imaging (DTI) data. Numerical simulations and suggestions for further elaboration are provided.

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