scholarly journals Onsager symmetry relations and the maximum number of propagating hydrodynamic modes

1974 ◽  
Vol 9 (1) ◽  
pp. 431-434 ◽  
Author(s):  
H. N. W. Lekkerkerker ◽  
W. G. Laidlaw
Keyword(s):  
Hydrodynamic Modes ◽  
Onsager Symmetry ◽  
Symmetry Relations

scholarly journals A nonlinear thermodynamic model for a breakdown of the Onsager symmetry and the efficiency of thermoelectric conversion in nanowires

2014 ◽  
Vol 470 (2170) ◽  
pp. 20140265 ◽  
Author(s):  
V. A. Cimmelli ◽  
A. Sellitto ◽  
D. Jou
Keyword(s):  
Transport Coefficients ◽  
Thermoelectric Conversion ◽  
Thermoelectric Energy ◽  
Thermoelectric Systems ◽  
Onsager Symmetry ◽  
Effective Transport ◽  
Non Local ◽  
Effective Transport Coefficients ◽  
Linear Effects ◽  
Symmetry Relations

We consider non-equilibrium steady-state situations for thermoelectric systems with non-local and non-linear effects. We show that the Onsager symmetry relations for effective transport coefficients break down. We also estimate the consequences of such a breakdown for the efficiency of the thermoelectric energy conversion which, under some conditions, could be higher than in the usual linear regime with Onsager symmetry.

scholarly journals Thermoelectric Thomson Relations Revisited for a Linear Energy Converter

2019 ◽  
Vol 44 (3) ◽  
pp. 315-332 ◽  
Author(s):  
Saul Gonzalez-Hernandez ◽  
Luis-Antonio Arias-Hernandez
Keyword(s):  
Electric Conductivity ◽  
Heat Engine ◽  
Irreversible Thermodynamic ◽  
Steady States ◽  
Energy Converter ◽  
Onsager Symmetry ◽  
Microscopic Models ◽  
Type Relation ◽  
Phenomenological Coefficients ◽  
Symmetry Relations

Abstract In this paper we revisit the classic thermocouple model, as a Linear Irreversible Thermodynamic (LIT) energy converter. In this model we have two types of phenomenological coefficients: the first comes from some microscopic models, such as the coefficient associated with the electric conductivity, and the second comes from experimental facts, such as the coefficient associated with the Seebeck power. We show that in the last case, these coefficients can be related to the thermodynamic operation modes of the energy converter. These relations between the experimental phenomenological coefficients and the regimes of performance allow us to propose a first and a second Thomson-type relation, which give us 12 new relations between the Seebeck power, the Peltier heat and the Thomson heat. With this purpose we develop the idea of non-isothermal linear energy converters operated either “directly” (like a heat engine) or “inversely” (like a refrigerator). We analyze the energetics associated to these converters operating under steady states corresponding to different modes of performance, all of them satisfying the fundamental Onsager symmetry relations.

scholarly journals Ramanujan’s function k(τ)=r(τ)r 2(2τ) and its modularity

2020 ◽  
Vol 18 (1) ◽  
pp. 1727-1741
Author(s):  
Yoonjin Lee ◽  
Yoon Kyung Park
Keyword(s):  
Continued Fraction ◽  
Quadratic Field ◽  
Singular Values ◽  
Modular Function ◽  
Imaginary Quadratic Field ◽  
Modular Equations ◽  
Positive Rational Number ◽  
Congruence Relations ◽  
Symmetry Relations ◽  
Ray Class Field

Abstract We study the modularity of Ramanujan’s function k ( τ ) = r ( τ ) r 2 ( 2 τ ) k(\tau )=r(\tau ){r}^{2}(2\tau ) , where r ( τ ) r(\tau ) is the Rogers-Ramanujan continued fraction. We first find the modular equation of k ( τ ) k(\tau ) of “an” level, and we obtain some symmetry relations and some congruence relations which are satisfied by the modular equations; these relations are quite useful for reduction of the computation cost for finding the modular equations. We also show that for some τ \tau in an imaginary quadratic field, the value k ( τ ) k(\tau ) generates the ray class field over an imaginary quadratic field modulo 10; this is because the function k is a generator of the field of the modular function on Γ 1 ( 10 ) {{\mathrm{\Gamma}}}_{1}(10) . Furthermore, we suggest a rather optimal way of evaluating the singular values of k ( τ ) k(\tau ) using the modular equations in the following two ways: one is that if j ( τ ) j(\tau ) is the elliptic modular function, then one can explicitly evaluate the value k ( τ ) k(\tau ) , and the other is that once the value k ( τ ) k(\tau ) is given, we can obtain the value k ( r τ ) k(r\tau ) for any positive rational number r immediately.

scholarly journals Critical behaviour of hydrodynamic series

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
M. Asadi ◽  
H. Soltanpanahi ◽  
F. Taghinavaz
Keyword(s):  
Chemical Potential ◽  
Transport Coefficients ◽  
Hydrodynamic Modes ◽  
Third Order ◽  
Hydrodynamic Mode ◽  
Strongly Coupled ◽  
Conformal Theory ◽  
Shear Dispersion ◽  
Type Iib String Theory ◽  
Hydrodynamic Transport

Abstract We investigate the time-dependent perturbations of strongly coupled $$ \mathcal{N} $$ N = 4 SYM theory at finite temperature and finite chemical potential with a second order phase transition. This theory is modelled by a top-down Einstein-Maxwell-dilaton description which is a consistent truncation of the dimensional reduction of type IIB string theory on AdS5×S5. We focus on spin-1 and spin-2 sectors of perturbations and compute the linearized hydrodynamic transport coefficients up to the third order in gradient expansion. We also determine the radius of convergence of the hydrodynamic mode in spin-1 sector and the lowest non-hydrodynamic modes in spin-2 sector. Analytically, we find that all the hydrodynamic quantities have the same critical exponent near the critical point θ = $$ \frac{1}{2} $$ 1 2 . Moreover, we propose a relation between symmetry enhancement of the underlying theory and vanishing of the only third order hydrodynamic transport coefficient θ1, which appears in the shear dispersion relation of a conformal theory on a flat background.

scholarly journals An explicit construction of the dimension-9 operator basis in the standard model effective field theory

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Yi Liao ◽  
Xiao-Dong Ma
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Effective Field Theory ◽  
Equations Of Motion ◽  
Baryon Number ◽  
Explicit Construction ◽  
Effective Field ◽  
Starting Point ◽  
The Standard Model ◽  
Symmetry Relations

Abstract We investigate systematically dimension-9 operators in the standard model effective field theory which contains only standard model fields and respects its gauge symmetry. With the help of the Hilbert series approach to classifying operators according to their lepton and baryon numbers and their field contents, we construct the basis of operators explicitly. We remove redundant operators by employing various kinematic and algebraic relations including integration by parts, equations of motion, Schouten identities, Dirac matrix and Fierz identities, and Bianchi identities. We confirm counting of independent operators by analyzing their flavor symmetry relations. All operators violate lepton or baryon number or both, and are thus non-Hermitian. Including Hermitian conjugated operators there are $$ {\left.384\right|}_{\Delta B=0}^{\Delta L=\pm 2}+{\left.10\right|}_{\Delta B=\pm 2}^{\Delta L=0}+{\left.4\right|}_{\Delta B=\pm 1}^{\Delta L=\pm 3}+{\left.236\right|}_{\Delta B=\pm 1}^{\Delta L=\mp 1} $$ 384 Δ B = 0 Δ L = ± 2 + 10 Δ B = ± 2 Δ L = 0 + 4 Δ B = ± 1 Δ L = ± 3 + 236 Δ B = ± 1 Δ L = ∓ 1 operators without referring to fermion generations, and $$ {\left.44874\right|}_{\Delta B=0}^{\Delta L=\pm 2}+{\left.2862\right|}_{\Delta B=\pm 2}^{\Delta L=0}+{\left.486\right|}_{\Delta B=\pm 1}^{\Delta L=\pm 3}+{\left.42234\right|}_{\Delta B=\mp 1}^{\Delta L=\pm 1} $$ 44874 Δ B = 0 Δ L = ± 2 + 2862 Δ B = ± 2 Δ L = 0 + 486 Δ B = ± 1 Δ L = ± 3 + 42234 Δ B = ∓ 1 Δ L = ± 1 operators when three generations of fermions are referred to, where ∆L, ∆B denote the net lepton and baryon numbers of the operators. Our result provides a starting point for consistent phenomenological studies associated with dimension-9 operators.

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