scholarly journals MATHEMATICAL DESCRIPTION OF THE NON-EQUILIBRIUM STATE OF SYMMETRIC PARTICLE SYSTEMS

2019 ◽  
Vol 32 (5) ◽  
Author(s):  
H.M. Hubal
Keyword(s):  
Equilibrium State ◽  
Mathematical Description ◽  
Particle Systems ◽  
Non Equilibrium

scholarly journals Non-universal dynamics of staggered non-equilibrium particle systems and Ising chains

1998 ◽  
Vol 31 (2) ◽  
pp. 541-549 ◽  
Author(s):  
R B Stinchcombe ◽  
J E Santos ◽  
M D Grynberg
Keyword(s):  
Particle Systems ◽  
Non Equilibrium

Ostwald´s Rule and the Principle of the Shortest Way

2010 ◽  
Vol 224 (06) ◽  
pp. 929-934 ◽  
Author(s):  
Herbert W. Zimmermann
Keyword(s):  
Melting Point ◽  
Equilibrium State ◽  
Entropy Production ◽  
Thermodynamic Stability ◽  
Lagrange Equation ◽  
Classical Mechanics ◽  
Geodesic Line ◽  
Final Equilibrium State ◽  
Relevant Variables ◽  
Non Equilibrium

AbstractWe consider a substance X with two monotropic modifications 1 and 2 of different thermodynamic stability ΔH1 < ΔH2. Ostwald´s rule states that first of all the instable modification 1 crystallizes on cooling down liquid X, which subsequently turns into the stable modification 2. Numerous examples verify this rule, however what is its reason? Ostwald´s rule can be traced back to the principle of the shortest way. We start with Hamilton´s principle and the Euler-Lagrange equation of classical mechanics and adapt it to thermodynamics. Now the relevant variables are the entropy S, the entropy production P = dS/dt, and the time t. Application of the Lagrangian F(S, P, t) leads us to the geodesic line S(t). The system moves along the geodesic line on the shortest way I from its initial non-equilibrium state i of entropy Si to the final equilibrium state f of entropy Sf. The two modifications 1 and 2 take different ways I1 and I2. According to the principle of the shortest way, I1 < I2 is realized in the first step of crystallization only. Now we consider a supercooled sample of liquid X at a temperature T just below the melting point of 1 and 2. Then the change of entropy ΔS1 = Sf 1 - Si 1 on crystallizing 1 can be related to the corresponding chang of enthalpy by ΔS1 = ΔH1/T. Now it can be shown that the shortest way of crystallization I1 corresponds under special, well-defined conditions to the smallest change of entropy ΔS1 < ΔS2 and thus enthalpy ΔH1 < ΔH2. In other words, the shortest way of crystallization I1 really leads us to the instable modification 1. This is Ostwald´s rule.

Extended Thermodynamic Approach for Non-Equilibrium Gas Flow

2013 ◽  
Vol 13 (5) ◽  
pp. 1330-1356 ◽  
Author(s):  
G. H. Tang ◽  
G. X. Zhai ◽  
W. Q. Tao ◽  
X. J. Gu ◽  
D. R. Emerson
Keyword(s):  
Heat Transfer ◽  
Equilibrium State ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Flow Characteristics ◽  
Bimodal Distribution ◽  
Thermodynamic Approach ◽  
Navier Stokes ◽  
Extended Thermodynamic ◽  
Non Equilibrium

AbstractGases in microfluidic structures or devices are often in a non-equilibrium state. The conventional thermodynamic models for fluids and heat transfer break down and the Navier-Stokes-Fourier equations are no longer accurate or valid. In this paper, the extended thermodynamic approach is employed to study the rarefied gas flow in microstructures, including the heat transfer between a parallel channel andpressure-driven Poiseuille flows through a parallel microchannel andcircular microtube. The gas flow characteristics are studied and it is shown that the heat transfer in the non-equilibrium state no longer obeys the Fourier gradient transport law. In addition, the bimodal distribution of streamwise and spanwise velocity and temperature through a long circular microtube is captured for the first time.

scholarly journals Influence of the β-particle flux and UV-irradiation on the properties of alloys, being at the non-equilibrium state

2020 ◽  
Vol 1431 ◽  
pp. 012011
Author(s):  
V A Fedorov ◽  
M V Boytsova ◽  
T N Pluzhnikova ◽  
A D Berezner
Keyword(s):  
Equilibrium State ◽  
Uv Irradiation ◽  
Particle Flux ◽  
Non Equilibrium

scholarly journals The slow relaxation of non-equilibrium state in metal target excited by picosecond electron beam: interferometric and simulation studies

2018 ◽  
Vol 1115 ◽  
pp. 022007
Author(s):  
S V Barakhvostov ◽  
N B Volkov ◽  
A I Lipchak ◽  
V P Tarakanov ◽  
S I Tkachenko ◽  
...  
Keyword(s):  
Electron Beam ◽  
Equilibrium State ◽  
Slow Relaxation ◽  
Simulation Studies ◽  
Metal Target ◽  
Non Equilibrium

The Influence of Discharge Capillary Size, Distance, and Gas Composition on the Non-Equilibrium State of Microplasma

2016 ◽  
Vol 13 (7) ◽  
pp. 690-697 ◽  
Author(s):  
Asif Majeed ◽  
Xiaoxia Zhong ◽  
Shaofeng Xu ◽  
Xinhui Wu ◽  
Uros Cvelbar ◽  
...  
Keyword(s):  
Equilibrium State ◽  
Gas Composition ◽  
Capillary Size ◽  
Non Equilibrium
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