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.

The Effects of Vibrational Relaxation on Hypersonic Flow Past Blunt Bodies

1997 ◽  
Vol 14 (4) ◽  
pp. 357-373 ◽  
Author(s):  
P. A. Blythe
Keyword(s):  
Hypersonic Flow ◽  
Vibrational Relaxation ◽  
Bluff Body ◽  
Flow Past ◽  
Equilibrium Parameter ◽  
Blunt Bodies ◽  
Relaxing Gas ◽  
Non Equilibrium

SummaryThe analysis of Freeman is extended to the hypersonic flow of an inviscid, vibrationally relaxing gas past a bluff body. Expressions for the shock shape, streamline shapes and stand-off distance are derived; these expressions have been evaluated for a sphere for various values of an appropriate non-equilibrium parameter Λ.

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.

Two-Phase Critical Flow Simulations by Using a New Non-Equilibrium Model and a Modified Equilibrium Model

2010 ◽  
Author(s):  
Moon-Sun Chung ◽  
Sung-Jae Yi ◽  
Keun-Shik Chang
Keyword(s):  
Phase Change ◽  
Equilibrium Model ◽  
Phase Changes ◽  
Critical Flow ◽  
Vapor Generation ◽  
Two Phase ◽  
Subcooled Liquid ◽  
Equilibrium Parameter ◽  
Phase Mixture ◽  
Non Equilibrium

An accurate prediction of a critical flow discharged from a pressurized pipe system is of most importance in such a safety analysis of nuclear power plants, since it provides the transient boundary conditions during the depressurization transients initiated by a pipe break in primary or secondary systems and during the over-pressurization transients resulting in a relief of coolant through valves. Mass and energy discharge through the opening of pressure boundary affects the system thermal hydraulic responses, that is, phase changes and flow distribution in the system, and the mass inventory remaining in the system necessary to remove core decay heat of a nuclear reactor. Therefore, the safety significance relating to the critical flow led to a development of various empirical and mechanistic critical flow models. However, the accuracies of these models are still in question especially during two-phase critical flow condition. A good example of that is a homogeneous equilibrium model (HEM). The HEM is the basis of several system codes, such as early versions of RELAP, for nuclear loss-of-coolant accident (LOCA). The major non-equilibrium phenomena that are ignored in the HEM are vapor bubble nucleation and interface heat, mass, and momentum transfer. Henry-Fauske empirically handled non-equilibrium vapor generation by introducing a non-equilibrium parameter that allows only a fraction of the equilibrium vapor generation to occur. This approach boils down in essence to a correlation of the deviation between the measured flow rate and the prediction from the HEM: The details of the flow path do not have to be worked out and only needs to know the upstream conditions. However, if we treat non-equilibrium phenomena with this model, it requires an empirical database of the non-equilibrium parameters or their correlations that are so far unknown. Further, because the coefficients are not applied separately to the subcooled liquid and two-phase mixture, we have not been able to treat the non-equilibrium phenomena with the phase change properly. For this reason, we propose the non-equilibrium parameters for subcooled liquid and two-phase mixture, respectively, and then we adopt their combinations according to the flow conditions through the phase change process using the RELAP5/MOD3 code. In addition, we discuss the assessment results of Marviken LBLOCA tests using these non-equilibrium parameter sets with those from the non-equilibrium model by Trapp-Ransom and Chung et al.

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