Capture rate and efficiency of an oscillating non-ideal trap interacting with a sea of random diffusing particles. A non-equilibrium Fokker–Planck picture

2015 ◽  
Vol 379 (4) ◽  
pp. 241-245 ◽  
Author(s):  
A. Grassi ◽  
G.M. Lombardo ◽  
M. Pannuzzo ◽  
A. Raudino
Keyword(s):  
Capture Rate ◽  
Non Equilibrium ◽  
Fokker Planck

scholarly journals Non-equilibrium parameter for a hybrid Fokker-Planck/DSMC scheme

2019 ◽  
Author(s):  
Christian Hepp ◽  
Martin Grabe ◽  
Klaus Hannemann
Keyword(s):  
Equilibrium Parameter ◽  
Non Equilibrium ◽  
Fokker Planck

scholarly journals Entropy Production, Entropy Generation, and Fokker-Planck Equations for Cancer Cell Growth

Physics ◽  
2019 ◽  
Vol 1 (1) ◽  
pp. 147-153
Author(s):  
Salvatore Capotosto ◽  
Bailey Smoot ◽  
Randal Hallford ◽  
Preet Sharma
Keyword(s):  
Statistical Mechanics ◽  
Cancer Cells ◽  
Entropy Production ◽  
Cancer Cell ◽  
Entropy Generation ◽  
Normal Growth ◽  
Equilibrium Statistical Mechanics ◽  
Fokker Planck Equations ◽  
Non Equilibrium ◽  
Fokker Planck

It is rather difficult to understand biological systems from a physics point of view, and understanding systems such as cancer is even more challenging. There are many factors affecting the dynamics of a cancer cell, and they can be understood approximately. We can apply the principles of non-equilibrium statistical mechanics and thermodynamics to have a greater understanding of such systems. Very much like other systems, living systems also transform energy and matter during metabolism, and according to the First Law of Thermodynamics, this could be described as a capacity to transform energy in a controlled way. The properties of cancer cells are different from regular cells. Cancer is a name used for a set of malignant cells that lost control over normal growth. Cancer can be described as an open, complex, dynamic, and self-organizing system. Cancer is considered as a non-linear dynamic system, which can be explained to a good degree using techniques from non-equilibrium statistical mechanics and thermodynamics. We will also look at such a system through its entropy due to to the interaction with the environment and within the system itself. Here, we have studied the entropy generation versus the entropy production approach, and have calculated the entropy of growth of cancer cells using Fokker-Planck equations.

scholarly journals On the construction of a family of anomalous-diffusion Fokker–Planck−Kolmogorov’s equations based on the Sharma–Taneja–Mittal entropy functional

2021 ◽  
Vol 51 ◽  
pp. 74-95
Author(s):  
Aleksandr Vladimirovich Kolesnichenko
Keyword(s):  
Stochastic Systems ◽  
Probability Density Distribution ◽  
Convexity Property ◽  
Logical Scheme ◽  
Entropy Functional ◽  
Fpk Equation ◽  
Ansatz Approach ◽  
The Ansatz Approach ◽  
Non Equilibrium ◽  
Fokker Planck

A logical scheme for constructing thermodynamics of anomalous stochastic systems based on the nonextensive two-parameter (κ, ς) -entropy of Sharma–Taneja–Mittal (SHTM) is considered. Thermodynamics within the framework (2 - q) -statistics of Tsallis was constructed, which belongs to the STM family of statistics. The approach of linear nonequilibrium thermodynamics to the construction of a family of nonlinear equations of Fokker−Planck−Kolmogorov (FPK), is used, correlated with the entropy of the STM, in which the stationary solution of the diffusion equation coincides with the corresponding generalized Gibbs distribution obtained from the extremality (κ, ς) - entropy condition of a non-additive stochastic system. Taking into account the convexity property of the Bregman divergence, it was shown that the principle of maximum equilibrium entropy is valid for (κ, ς) - systems, and also was proved the H - theorem determining the direction of the time evolution of the non-equilibrium state of the system. This result is extended also to non-equilibrium systems that evolve to a stationary state in accordance with the nonlinear FPK equation. The method of the ansatz- approach for solving non-stationary FPK equations is considered, which allows us to find the time dependence of the probability density distribution function for non-equilibrium anomalous systems. Received diffusive equations FPК can be used, in particular, at the analysis of diffusion of every possible epidemics and pandemics. The obtained diffusion equations of the FPK can be used, in particular, in the analysis of the spread of various epidemics and pandemics.

Application of analytical electron microscopy to studies of equilibrium and non-equilibrium segregation in materials

1992 ◽  
Vol 50 (2) ◽  
pp. 1214-1215
Author(s):  
Edward A Kenik
Keyword(s):  
Electron Microscopy ◽  
Analytical Electron Microscopy ◽  
Extended Defects ◽  
Probe Diameter ◽  
Specimen Holder ◽  
Analytical Electron ◽  
Scanning Transmission ◽  
Solute Atoms ◽  
Equilibrium Segregation ◽  
Non Equilibrium

Segregation of solute atoms to grain boundaries, dislocations, and other extended defects can occur under thermal equilibrium or non-equilibrium conditions, such as quenching, irradiation, or precipitation. Generally, equilibrium segregation is narrow (near monolayer coverage at planar defects), whereas non-equilibrium segregation exhibits profiles of larger spatial extent, associated with diffusion of point defects or solute atoms. Analytical electron microscopy provides tools both to measure the segregation and to characterize the defect at which the segregation occurs. This is especially true of instruments that can achieve fine (<2 nm width), high current probes and as such, provide high spatial resolution analysis and characterization capability. Analysis was performed in a Philips EM400T/FEG operated in the scanning transmission mode with a probe diameter of <2 nm (FWTM). The instrument is equipped with EDAX 9100/70 energy dispersive X-ray spectrometry (EDXS) and Gatan 666 parallel detection electron energy loss spectrometry (PEELS) systems. A double-tilt, liquid-nitrogen-cooled specimen holder was employed for microanalysis in order to minimize contamination under the focussed spot.

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