The matrix model, a driven state variables approach to non-equilibrium thermodynamics

2001 ◽  
Vol 96 (1-2) ◽  
pp. 63-76 ◽  
Author(s):  
R.J.J. Jongschaap
Keyword(s):  
Matrix Model ◽  
State Variables ◽  
Equilibrium Thermodynamics ◽  
The Matrix ◽  
Non Equilibrium

scholarly journals A case study of non-Fourier heat conduction using internal variables and GENERIC

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mátyás Szücs ◽  
Michal Pavelka ◽  
Róbert Kovács ◽  
Tamás Fülöp ◽  
Péter Ván ◽  
...  
Keyword(s):  
Heat Conduction ◽  
General Equation ◽  
Internal Variables ◽  
State Variables ◽  
Equilibrium Thermodynamics ◽  
Ginzburg Landau ◽  
Entropy Current ◽  
Fourier Heat Conduction ◽  
Non Equilibrium

Abstract Applying simultaneously the methodology of non-equilibrium thermodynamics with internal variables (NET-IV) and the framework of General Equation for the Non-Equilibrium Reversible–Irreversible Coupling (GENERIC), we demonstrate that, in heat conduction theories, entropy current multipliers can be interpreted as relaxed state variables. Fourier’s law and its various extensions—the Maxwell–Cattaneo–Vernotte, Guyer–Krumhansl, Jeffreys type, Ginzburg–Landau (Allen–Cahn) type and ballistic–diffusive heat conduction equations—are derived in both formulations. Along these lines, a comparison of NET-IV and GENERIC is also performed. Our results may pave the way for microscopic/multiscale understanding of beyond-Fourier heat conduction and open new ways for numerical simulations of heat conduction problems.

A novel construction of thermodynamically compatible models and its correspondence with Boltzmann-equation-based moment-closure hierarchies

2015 ◽  
Vol 40 (4) ◽  
Author(s):  
Liu Hong ◽  
Zaibao Yang ◽  
Yi Zhu ◽  
Wen-An Yong
Keyword(s):  
Boltzmann Equation ◽  
Irreversible Thermodynamics ◽  
Moment Closure ◽  
State Variables ◽  
Balance Equations ◽  
Equilibrium Thermodynamics ◽  
Macroscopic Modeling ◽  
The Boltzmann Equation ◽  
Novel Approach ◽  
Non Equilibrium

AbstractIn this article, we propose a novel approach to construct macroscopic balance equations and constitutive equations describing various irreversible phenomena. It is based on the general principles of non-equilibrium thermodynamics and consists of four basic steps: picking suitable state variables, choosing a strictly concave entropy function, properly separating entropy fluxes and production rates, and determining a dissipation matrix. Our approach takes advantage of both extended irreversible thermodynamics and GENERIC formalisms and shows a direct correspondence with Levermore's moment-closure hierarchies for the Boltzmann equation. As a direct application, a new ten-moment model beyond the classical hierarchies is constructed and is shown to recover the Euler equations in the equilibrium state. These interesting results may put various macroscopic modeling approaches, starting from the general principles of non-equilibrium thermodynamics, on a solid microscopic foundation based on the Boltzmann equation.

Developing the basis of the matrix model of the regional innovation subsystem

2020 ◽  
Vol 18 (11) ◽  
pp. 2183-2204
Author(s):  
E.I. Moskvitina
Keyword(s):  
Russian Federation ◽  
Matrix Model ◽  
Federal District ◽  
Assessment Method ◽  
Expert Assessment ◽  
Regional Innovation ◽  
Regional Strategies ◽  
Analysis And Synthesis ◽  
The Matrix ◽  
The Russian Federation

Subject. This article deals with the issues related to the formation and implementation of the innovation capacity of the Russian Federation subjects. Objectives. The article aims to develop the organizational and methodological foundations for the formation of a model of the regional innovation subsystem. Methods. For the study, I used the methods of analysis and synthesis, economics and statistics analysis, and the expert assessment method. Results. The article presents a developed basis of the regional innovation subsystem matrix model. It helps determine the relationship between the subjects and the parameters of the regional innovation subsystem. To evaluate the indicators characterizing the selected parameters, the Volga Federal District regions are considered as a case study. The article defines the process of reconciliation of interests between the subjects of regional innovation. Conclusions. The results obtained can be used by regional executive bodies when developing regional strategies for the socio-economic advancement of the Russian Federation subjects.

scholarly journals Exact 1/N expansion of Wilson loop correlators in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Wolfgang Mück
Keyword(s):  
Matrix Model ◽  
Wilson Loop ◽  
Model Solution ◽  
Wilson Loops ◽  
Combinatorial Formula ◽  
Expectation Value ◽  
Yang Mills ◽  
Hooft Coupling ◽  
The Matrix ◽  
Super Yang Mills Theory

Abstract Supersymmetric circular Wilson loops in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory are discussed starting from their Gaussian matrix model representations. Previous results on the generating functions of Wilson loops are reviewed and extended to the more general case of two different loop contours, which is needed to discuss coincident loops with opposite orientations. A combinatorial formula representing the connected correlators of multiply wound Wilson loops in terms of the matrix model solution is derived. Two new results are obtained on the expectation value of the circular Wilson loop, the expansion of which into a series in 1/N and to all orders in the ’t Hooft coupling λ was derived by Drukker and Gross about twenty years ago. The connected correlators of two multiply wound Wilson loops with arbitrary winding numbers are calculated as a series in 1/N. The coefficient functions are derived not only as power series in λ, but also to all orders in λ by expressing them in terms of the coefficients of the Drukker and Gross series. This provides an efficient way to calculate the 1/N series, which can probably be generalized to higher-point correlators.

scholarly journals Divergent ⇒ complex amplitudes in two dimensional string theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Matrix Model ◽  
Two Dimensional ◽  
Full Matrix ◽  
Instanton Contribution ◽  
The Matrix ◽  
Theory Result ◽  
The One ◽  
Remarkable Agreement

Abstract In a recent paper, Balthazar, Rodriguez and Yin found remarkable agreement between the one instanton contribution to the scattering amplitudes of two dimensional string theory and those in the matrix model to the first subleading order. The comparison was carried out numerically by analytically continuing the external energies to imaginary values, since for real energies the string theory result diverges. We use insights from string field theory to give finite expressions for the string theory amplitudes for real energies. We also show analytically that the imaginary parts of the string theory amplitudes computed this way reproduce the full matrix model results for general scattering amplitudes involving multiple closed strings.

scholarly journals Contraction of polymer gels created by the activity of molecular motors

Soft Matter ◽  
2019 ◽  
Vol 15 (22) ◽  
pp. 4467-4475 ◽  
Author(s):  
Mattia Bacca ◽  
Omar A. Saleh ◽  
Robert M. McMeeking
Keyword(s):  
Mechanical Behavior ◽  
Molecular Motors ◽  
Polymer Gels ◽  
Polymer Gel ◽  
Equilibrium Thermodynamics ◽  
Non Equilibrium

We propose a theory based on non-equilibrium thermodynamics to describe the mechanical behavior of an active polymer gel created by the inclusion of molecular motors in its solvent.

scholarly journals Why Is the Matrix Model Correct?

1997 ◽  
Vol 79 (19) ◽  
pp. 3577-3580 ◽  
Author(s):  
Nathan Seiberg
Keyword(s):  
Matrix Model ◽  
The Matrix
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