scholarly journals Non-equilibrium phase and entanglement entropy in 2D holographic superconductors via gauge–string duality

2016 ◽  
Vol 94 (10) ◽  
pp. 1102-1111
Author(s):  
Najmeh Al Sadat Mazhari ◽  
Davood Momeni ◽  
Ratbay Myrzakulov ◽  
Hosein Gholizade ◽  
Muhammad Raza
Keyword(s):  
Entanglement Entropy ◽  
Equilibrium Phase ◽  
Approximate Solutions ◽  
Dynamical Instability ◽  
Holographic Superconductor ◽  
Maxwell Fields ◽  
Normal Mass ◽  
Definition Of ◽  
Log Ratio ◽  
Non Equilibrium

An alternative method of developing the theory of non-equilibrium two-dimensional holographic superconductor is to start from the definition of a time-dependent AdS3 background. As originally proposed, many of these formulae were cast in exponential form, but the adoption of the numeric method of expression throughout the bulk serves to show more clearly the relationship between the various parameters. The time dependence behavior of the scalar condensation and Maxwell fields are fitted numerically. A usual value for Maxwell field on AdS horizon is exp(–bt), and the exponential log ratio is therefore 10−8 s−1. The coefficient b of the time in the exponential term exp(–bt) can be interpreted as a tool to measure the degree of dynamical instability; its reciprocal 1/b is the time in which the disturbance is multiplied in the ratio. A discussion of some of the exponential formulae is given by the scalar field ψ(z, t) near the AdS boundary. It may be possible that a long interval would elapse in the system, which tends to the equilibrium state, where the normal mass and conformal dimensions emerged. A somewhat curious calculation has been made to illustrate the holographic entanglement entropy for this system. The foundation of all this calculation is, of course, a knowledge of multiple (connected and disconnected) extremal surfaces. There are several cases in which exact and approximate solutions are jointly used; a variable numerical quantity is represented by a graph, and the principles of approximation are then applied to determine related numerical quantities. In the case of the disconnected phase with a finite extremal area, we find a discontinuity in the first derivative of the entanglement entropy as the conserved charge J is increased.

Thermodynamic and Kinetic Calculation of Non-Equilibrium Microstructure Design of TRIP Steel

2014 ◽  
Vol 783-786 ◽  
pp. 766-770
Author(s):  
Yan Lin He ◽  
Na Qiong Zhu ◽  
Wei Sen Zheng ◽  
Xiao Gang Lu ◽  
Lin Li
Keyword(s):  
Trip Steel ◽  
Equilibrium Phase ◽  
Microstructure Design ◽  
Kinetic Calculation ◽  
Software Comparison ◽  
Thermo Calc Software ◽  
Curve Determination ◽  
Equilibrium Microstructure ◽  
The Relationship ◽  
Non Equilibrium

The non-equilibrium microstructure of Fe-C-Mn-Si TRIP steel is designed bythermodynamic and kinetic calculation. The upper limit of bainitic transformation temperature iscalculated and compared to that characterized by CCT curve determination. s M temperature isdetermined based on thermodynamics of martensitic transformation and sublattice model. Thecalculation is conducted via TQ6-patch in Thermo-Calc software. Comparison between thecalculations and experiments reveals the relationship between non-equilibrium phase compositionand heat treatment parameters which can be utilized to achieve the elaborate design of alloy and heattreatment for super TRIP steel.

scholarly journals Equilibrium electrochemical synthesis diagrams of systems, forming homogeneous alloys and compounds

2003 ◽  
Vol 39 (1-2) ◽  
pp. 383-405 ◽  
Author(s):  
G. Kaptay
Keyword(s):  
Thermodynamic Parameter ◽  
Electrochemical Synthesis ◽  
Equilibrium Phase ◽  
Equilibrium Composition ◽  
Alloy Formation ◽  
Fixed Temperature ◽  
Synthesis Conditions ◽  
Melt Composition ◽  
Alloys And Compounds ◽  
Non Equilibrium

In the present paper thermodynamic limitations will be derived and summarized in the form of Equilibrium Electrochemical Synthesis (EES) diagrams, in order to predict the composition of the equilibrium phase, synthesized by galvanostatic co-deposition of components on inert electrodes. As a thermodynamic parameter, a difference of deposition potentials of pure components ( ?E) on inert cathodes is used (this parameter is a function of melt composition and temperature). Generally, the EES diagram predicts the equilibrium composition of the alloy as function temperature and ?E. However, for systems with homogeneous alloy formation the composition- ?E diagrams, drawn at a fixed temperature are more informative. As examples EES diagrams are constructed for the liquid Mg-Nd alloy, for some A(III)-B(V) (where A = Al, Ga, In and B = As, Sb), Si-C and for the Al-Ti system. For the Al-rich part of the Al-Ti system, also a semi-schematic non-equilibrium ES diagram is constructed. Based on these diagrams, the synthesis conditions of various phases has been discussed.

scholarly journals Thermodynamic Analysis of Relaxation Model for Non-Equilibrium Phase Behavior of Hydrocarbon Mixtures

2021 ◽  
Vol 2090 (1) ◽  
pp. 012138
Author(s):  
I M Indrupskiy ◽  
P A Chageeva
Keyword(s):  
Relaxation Time ◽  
Phase Behavior ◽  
Relaxation Process ◽  
Thermodynamic Analysis ◽  
Balance Equation ◽  
Equilibrium Phase ◽  
Characteristic Relaxation Time ◽  
Relaxation Model ◽  
Entropy Balance ◽  
Non Equilibrium

Abstract Mathematical models of phase behavior are widely used to describe multiphase oil and gas-condensate systems during hydrocarbon recovery from natural petroleum reservoirs. Previously a non-equilibrium phase behavior model was proposed as an extension over generally adopted equilibrium models. It is based on relaxation of component chemical potentials difference between phases and provides accurate calculations in some typical situations when non-instantaneous changing of phase fractions and compositions in response to variations of pressure or total composition is to be considered. In this paper we present a thermodynamic analysis of the relaxation model. General equations of non-equilibrium thermodynamics for multiphase flows in porous media are considered, and reduced entropy balance equation for the relaxation process is obtained. Isotropic relaxation process is simulated for a real multicomponent hydrocarbon system with different values of characteristic relaxation time using the non-equilibrium model implemented in the PVT Designer module of the RFD tNavigator simulation software. The results are processed with a special algorithm implemented in Matlab to calculate graphs of the total entropy time derivative and its constituents in the entropy balance equation. It is shown that the constituents have different signs, and the greatest influence on the entropy is associated with the interphase flow of the major component of the mixture and the change of the total system volume in the isotropic process. The characteristic relaxation time affects the rate at which the entropy is approaching its maximum value.

scholarly journals Response theory and phase transitions for the thermodynamic limit of interacting identical systems

2020 ◽  
Vol 476 (2244) ◽  
pp. 20200688
Author(s):  
Valerio Lucarini ◽  
Grigorios A. Pavliotis ◽  
Niccolò Zagli
Keyword(s):  
Phase Transitions ◽  
Thermodynamic Limit ◽  
Linear Response ◽  
Equilibrium Phase ◽  
Mean Field ◽  
Critical Transitions ◽  
Autocorrelation Time ◽  
The Common ◽  
Fokker Planck Equations ◽  
Non Equilibrium

We study the response to perturbations in the thermodynamic limit of a network of coupled identical agents undergoing a stochastic evolution which, in general, describes non-equilibrium conditions. All systems are nudged towards the common centre of mass. We derive Kramers–Kronig relations and sum rules for the linear susceptibilities obtained through mean field Fokker–Planck equations and then propose corrections relevant for the macroscopic case, which incorporates in a self-consistent way the effect of the mutual interaction between the systems. Such an interaction creates a memory effect. We are able to derive conditions determining the occurrence of phase transitions specifically due to system-to-system interactions. Such phase transitions exist in the thermodynamic limit and are associated with the divergence of the linear response but are not accompanied by the divergence in the integrated autocorrelation time for a suitably defined observable. We clarify that such endogenous phase transitions are fundamentally different from other pathologies in the linear response that can be framed in the context of critical transitions. Finally, we show how our results can elucidate the properties of the Desai–Zwanzig model and of the Bonilla–Casado–Morillo model, which feature paradigmatic equilibrium and non-equilibrium phase transitions, respectively.

scholarly journals Construction of a Class of Copula Using the Finite Difference Method

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Remi Guillaume Bagré ◽  
Frédéric Béré ◽  
Vini Yves Bernadin Loyara
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Numerical Scheme ◽  
Approximate Solutions ◽  
Copula Function ◽  
Common Technique ◽  
The Finite Difference Method ◽  
Definition Of ◽  
General Method

The definition of a copula function and the study of its properties are at the same time not obvious tasks, as there is no general method for constructing them. In this paper, we present a method that allows us to obtain a class of copula as a solution to a boundary value problem. For this, we use the finite difference method which is a common technique for finding approximate solutions of partial differential equations which consists in solving a system of relations (numerical scheme) linking the values of the unknown functions at certain points sufficiently close to each other.

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