Formatting Elliptic Model From SST k-ω Closure

2021 ◽  
pp. 1-15
Author(s):  
M. M. Rahman ◽  
Xinming Li ◽  
K. Hasan ◽  
Ming Lv
Keyword(s):  
Elliptic Model

Diffusive-dispersive travelling waves and kinetic relations. II A hyperbolic–elliptic model of phase-transition dynamics

2002 ◽  
Vol 132 (3) ◽  
pp. 545-565 ◽  
Author(s):  
Nabil Bedjaoui ◽  
Philippe G. LeFloch
Keyword(s):  
Phase Transition ◽  
Travelling Waves ◽  
Asymptotic Properties ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Phase Boundaries ◽  
Transition Dynamics ◽  
Nonlinear Viscosity ◽  
Kinetic Relations ◽  
Elliptic Model

We deal here with a mixed (hyperbolic-elliptic) system of two conservation laws modelling phase-transition dynamics in solids undergoing phase transformations. These equations include nonlinear viscosity and capillarity terms. We establish general results concerning the existence, uniqueness and asymptotic properties of the corresponding travelling wave solutions. In particular, we determine their behaviour in the limits of dominant diffusion, dominant dispersion or asymptotically small or large shock strength. As the viscosity and capillarity parameters tend to zero, the travelling waves converge to propagating discontinuities, which are either classical shock waves or supersonic phase boundaries satisfying the Lax and Liu entropy criteria, or else are undercompressive subsonic phase boundaries. The latter are uniquely characterized by the so-called kinetic function, whose properties are investigated in detail here.

scholarly journals On Cherednik and Nazarov-Sklyanin large N limit construction for integrable many-body systems with elliptic dependence on momenta

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
A. Grekov ◽  
A. Zotov
Keyword(s):  
Explicit Expression ◽  
Generating Function ◽  
Infinite Number ◽  
Symmetric Functions ◽  
Many Body ◽  
Quantum Double ◽  
Large N ◽  
Elliptic Model ◽  
Many Body Systems ◽  
Number Of Particles

Abstract The infinite number of particles limit in the dual to elliptic Ruijsenaars model (coordinate trigonometric degeneration of quantum double elliptic model) is proposed using the Nazarov-Sklyanin approach. For this purpose we describe double-elliptization of the Cherednik construction. Namely, we derive explicit expression in terms of the Cherednik operators, which reduces to the generating function of Dell commuting Hamiltonians on the space of symmetric functions. Although the double elliptic Cherednik operators do not commute, they can be used for construction of the N → ∞ limit.

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