scholarly journals Landau levels in wrinkled and rippled graphene sheets

2019 ◽  
Vol 30 (10) ◽  
pp. 1941006
Author(s):  
Kyriakos Flouris ◽  
Miller Mendoza Jimenez ◽  
Hans J. Herrmann
Keyword(s):  
Lattice Boltzmann ◽  
Energy Levels ◽  
Landau Levels ◽  
Graphene Sheets ◽  
Discrete Energy ◽  
Curved Manifolds ◽  
Average Deformation ◽  
Energy Quantum ◽  
Boltzmann Method ◽  
Realistic Geometries

We study the discrete energy spectrum of curved graphene sheets in the presence of a magnetic field. The shifting of the Landau levels is determined for complex and realistic geometries of curved graphene sheets. The energy levels follow a similar square root dependence on the energy quantum number as for rippled and flat graphene sheets. The Landau levels are shifted towards lower energies proportionally to the average deformation and the effect is larger compared to a simple uni-axially rippled geometry. Furthermore, the resistivity of wrinkled graphene sheets is calculated for different average space curvatures and shown to obey a linear relation. The study is carried out with a quantum lattice Boltzmann method, solving the Dirac equation on curved manifolds.

scholarly journals Quantized Alternate Current on Curved Graphene

2019 ◽  
Vol 4 (2) ◽  
pp. 39 ◽  
Author(s):  
Kyriakos Flouris ◽  
Sauro Succi ◽  
Hans J. Herrmann
Keyword(s):  
Lattice Boltzmann ◽  
Quantum Information Processing ◽  
Alternate Current ◽  
Real Space ◽  
Graphene Sheets ◽  
Curved Space ◽  
Berry Curvature ◽  
Space Curvature ◽  
Processing Algorithms ◽  
Boltzmann Method

Based on the numerical solution of the Quantum Lattice Boltzmann Method in curved space, we predicted the onset of a quantized alternating current on curved graphene sheets. This numerical prediction was verified analytically via a set of semi-classical equations that related the Berry curvature to real space curvature. The proposed quantized oscillating current on curved graphene could form the basis for the implementation of quantum information-processing algorithms.

scholarly journals Direct numerical simulation of transitional pulsatile stenotic flow using Lattice Boltzmann Method

2015 ◽  
Author(s):  
Kartik Jain
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Direct Numerical Simulations ◽  
Transitional Flow ◽  
Transitional Flows ◽  
Flow Through ◽  
Simulation Results ◽  
Boltzmann Method ◽  
Realistic Geometries

In the present work, I perform direct numerical simulations of pulsatile flow through a 75% eccentric stenosis using the Lattice Boltzmann Method. The stenosis was studied by Varghese et al. (2007b) in a benchmark computation and the goal of this work is to validate the LBM solver Musubi for transitional flows in anatomically realistic geometries. Whereas most of the study reproduces and compares simulation results from Musubi against the benchmark, the latter part quantifies the Kolmogorov micro-scales and discusses the role of space and time resolutions for the simulation of a transitional flow. The LBM results show an excellent agreement with the previously published results thereby increasing confidence on our Musubi solver for the simulation of transitional flows. The aim of this study is not to compare the computational efficiency of the code or the method but only the physics of the flow.

scholarly journals Direct numerical simulation of transitional pulsatile stenotic flow using Lattice Boltzmann Method

2016 ◽  
Author(s):  
Kartik Jain
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Direct Numerical Simulations ◽  
Complex Geometries ◽  
Present Contribution ◽  
Transitional Flows ◽  
Flow Through ◽  
Simulation Results ◽  
Boltzmann Method ◽  
Realistic Geometries

The present contribution reports direct numerical simulations of pulsatile flow through a 75% eccentric stenosis using the Lattice Boltzmann Method (LBM). The stenosis was previously studied by Varghese, Frankel, and Fischer in a benchmark computation, and the goal of this work is to evaluate the LBM and the solver Musubi for transitional flows in anatomically realistic geometries. A part of the study compares the LBM simulation results against the benchmark and evaluates the efficacy of most basic LBM scheme for simulation of such flows. The novelty lies in the computation of Kolmogorov micro-scales by performing simulations that consist of up to ∼ 700 million cells. Recommendations on the choice of spatial and temporal resolutions for simulation of transitional flows in complex geometries naturally arise from the results. The LBM results show an excellent agreement with the previously published results thereby validating the method and the solver Musubi for the simulation of transitional flows. The study suggests that with a prudent calibration of the parameters, the LB method, due to its simplicity and compute efficiency has advantages for the simulation of such flows.

scholarly journals Direct numerical simulation of transitional pulsatile stenotic flow using Lattice Boltzmann Method

2015 ◽  
Author(s):  
Kartik Jain
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Direct Numerical Simulations ◽  
Transitional Flow ◽  
Transitional Flows ◽  
Flow Through ◽  
Simulation Results ◽  
Boltzmann Method ◽  
Realistic Geometries

In the present work, I perform direct numerical simulations of pulsatile flow through a 75% eccentric stenosis using the Lattice Boltzmann Method. The stenosis was studied by Varghese et al. (2007b) in a benchmark computation and the goal of this work is to validate the LBM solver Musubi for transitional flows in anatomically realistic geometries. Whereas most of the study reproduces and compares simulation results from Musubi against the benchmark, the latter part quantifies the Kolmogorov micro-scales and discusses the role of space and time resolutions for the simulation of a transitional flow. The LBM results show an excellent agreement with the previously published results thereby increasing confidence on our Musubi solver for the simulation of transitional flows. The aim of this study is not to compare the computational efficiency of the code or the method but only the physics of the flow.

scholarly journals Direct numerical simulation of transitional pulsatile stenotic flow using Lattice Boltzmann Method

2016 ◽  
Author(s):  
Kartik Jain
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Direct Numerical Simulations ◽  
Complex Geometries ◽  
Present Contribution ◽  
Transitional Flows ◽  
Flow Through ◽  
Simulation Results ◽  
Boltzmann Method ◽  
Realistic Geometries

The present contribution reports direct numerical simulations of pulsatile flow through a 75% eccentric stenosis using the Lattice Boltzmann Method (LBM). The stenosis was previously studied by Varghese, Frankel, and Fischer in a benchmark computation, and the goal of this work is to evaluate the LBM and the solver Musubi for transitional flows in anatomically realistic geometries. A part of the study compares the LBM simulation results against the benchmark and evaluates the efficacy of most basic LBM scheme for simulation of such flows. The novelty lies in the computation of Kolmogorov micro-scales by performing simulations that consist of up to ∼ 700 million cells. Recommendations on the choice of spatial and temporal resolutions for simulation of transitional flows in complex geometries naturally arise from the results. The LBM results show an excellent agreement with the previously published results thereby validating the method and the solver Musubi for the simulation of transitional flows. The study suggests that with a prudent calibration of the parameters, the LB method, due to its simplicity and compute efficiency has advantages for the simulation of such flows.

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