A fluctuating lattice Boltzmann scheme for the one-dimensional KPZ equation

2012 ◽  
Vol 391 (20) ◽  
pp. 4557-4563 ◽  
Author(s):  
Vadzim Yermakou ◽  
Sauro Succi
Keyword(s):  
Lattice Boltzmann ◽  
Kpz Equation ◽  
One Dimensional ◽  
The One ◽  
Lattice Boltzmann Scheme

ONE-DIMENSIONAL QUANTUM LATTICE BOLTZMANN SCHEME FOR THE NONLINEAR DIRAC EQUATION

2013 ◽  
Vol 24 (12) ◽  
pp. 1340001 ◽  
Author(s):  
SILVIA PALPACELLI ◽  
PAUL ROMATSCHKE ◽  
SAURO SUCCI
Keyword(s):  
Dirac Equation ◽  
Lattice Boltzmann ◽  
Spontaneous Breaking ◽  
Mass Generation ◽  
Quantum Lattice ◽  
One Dimensional ◽  
Dynamic Mass ◽  
Nonlinear Dirac Equation ◽  
Njl Model ◽  
Lattice Boltzmann Scheme

We develop a quantum lattice Boltzmann (QLB) scheme for the Dirac equation with a nonlinear fermion interaction provided by the Nambu–Jona-Lasinio (NJL) model. Numerical simulations in 1 + 1 space-time dimensions, provide evidence of dynamic mass generation, through spontaneous breaking of chiral symmetry.

A SIMPLE METHOD TO CONSTRUCT LOCAL EQUILIBRIUM FUNCTION FOR LATTICE BOLTZMANN METHOD

2013 ◽  
Vol 24 (06) ◽  
pp. 1350038
Author(s):  
P. WANG ◽  
S. Q. ZHANG
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Local Equilibrium ◽  
New Method ◽  
Ratio Test ◽  
Simple Method ◽  
One Dimensional ◽  
Equilibrium Function ◽  
The One ◽  
Boltzmann Method

We have developed a simple method to construct local equilibrium function for lattice Boltzmann method (LBM). This new method can make LBM model satisfy compressible flow with a flexible specific-heat ratio. Test cases, including the one-dimensional Sod flow, one-dimensional Lax flow and thermal Couette flow are presented. Good results obtained using proposed new method, indicate that the proposed method is potentially capable of constructing of the local equilibrium function for LBM.

scholarly journals The One-Dimensional KPZ Equation and Its Universality Class

2015 ◽  
Vol 160 (4) ◽  
pp. 965-984 ◽  
Author(s):  
Jeremy Quastel ◽  
Herbert Spohn
Keyword(s):  
Universality Class ◽  
Kpz Equation ◽  
One Dimensional ◽  
The One
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