Preturbulent Regimes in Graphene Flow

Mendoza, M.; Herrmann, Hans J.; Succi, Sauro

doi:10.1103/physrevlett.106.156601

Cited by 88 publications

(109 citation statements)

References 17 publications

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“…This has suggested the possibility of observing pre-turbulent regimes, as explicitly pointed out in Ref. [10] and later confirmed by numerical simulations [11]. All these characteristics in graphene open up the possibility of studying several phenomena known from classical fluid dynamics, e.g.…”

Section: Introductionsupporting

confidence: 53%

Gaussian quadrature and lattice discretization of the Fermi-Dirac distribution for graphene

2013

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We construct a lattice kinetic scheme to study electronic flow in graphene. For this purpose, we first derive a basis of orthogonal polynomials, using as weight function the ultrarelativistic FermiDirac distribution at rest. Later, we use these polynomials to expand the respective distribution in a moving frame, for both cases, undoped and doped graphene. In order to discretize the Boltzmann equation and make feasible the numerical implementation, we reduce the number of discrete points in momentum space to 18 by applying a Gaussian quadrature, finding that the family of representative wave (2+1)-vectors, that satisfies the quadrature, reconstructs a honeycomb lattice. The procedure and discrete model are validated by solving the Riemann problem, finding excellent agreement with other numerical models. In addition, we have extended the Riemann problem to the case of different dopings, finding that by increasing the chemical potential, the electronic fluid behaves as if it increases its effective viscosity.

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Section: Introductionsupporting

confidence: 53%

Gaussian quadrature and lattice discretization of the Fermi-Dirac distribution for graphene

2013

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“…Full details can be found in the original references [39,40]. The scheme was validated for two different relativistic applications, 1d quark-gluon plasmas, 3d supernova explosions, and graphene [42], showing excellent performance on all of them. However, inherent to the moment-matching procedure, is the question of realizability, i.e.…”

Section: A Fully Relativistic Lb Algorithmmentioning

confidence: 99%

Fully relativistic lattice Boltzmann algorithm

2011

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Starting from the Maxwell-Jüttner equilibrium distribution, we develop a relativistic lattice Boltzmann (LB) algorithm capable of handling ultrarelativistic systems with flat, but expanding, spacetimes. The algorithm is validated through simulations of quark-gluon plasma, yielding excellent agreement with hydrodynamic simulations. The present scheme opens the possibility of transferring the recognized computational advantages of lattice kinetic theory to the context of both weakly and ultra-relativistic systems.PACS numbers: 47.75.+f, 47.11.-j Keywords: Relativistic fluid dynamics, Quark-gluon plasmas, Lattice Boltzmann I. MOTIVATIONThe great success of the Relativistic Heavy-Ion Collider (RHIC) experimental program [1][2][3][4] has provided the motivation to come up with realistic and quantitative simulations of heavy-ion collisions.Since the bulk of particles produced in relativistic heavy-ion collisions is described by fluid dynamics [5], the center-piece of any complete simulation attempt will involve a viscous fluid dynamics algorithm. The majority of presently available fluid dynamics codes is able to handle smooth initial conditions in 2+1 dimensions in the presence of shear viscosity [6][7][8][9][10]. However, it has by now been understood that the presence of event-by-event fluctuations in the initial state can lead to significantly different quantitative results with respect to smooth initial conditions [11], and may in some cases even explain qualitatively new phenomena. To be more specific, the presence of event-by-event fluctuations is the source of the non-vanishing elliptic flow found in RHIC experiments at central collisions, the source of hydrodynamic flow-fluctuations, and may (through the presence of socalled triangular flow v 3 ) naturally explain the presence of the 'ridge phenomenon' found in experiments [12][13][14][15]. Thus, it is probably fair to say that without including the effect of event-by-event fluctuations, a description of the medium created in heavy-ion collisions cannot be regarded as realistic. This provides the motivation to develop a fully relativistic and computationally efficient viscous fluid dynamics algorithm that can handle initial state fluctuations. Also, such an algorithm can be used Further motivation is provided by other systems where relativistic viscous fluid flows are of interest, such as astrophysical systems and condensed matter systems such as graphene [17]. One particular question that arises in all this different systems is when relativistic fluid flow becomes turbulent, which involves a determination of the critical Reynolds number and the turbulent spectrum [18,19]. II. LATTICE KINETIC APPROACH TO HYDRODYNAMICSFluid turbulence, both classical and relativistic, sets one of the most compelling challenges in modern computational physics. This motivates a relentless search for new and ever more efficient methods for solving the hydrodynamic equations of motion in the high-Reynolds turbulent regimes. In the last two decades, a new computational paradigm has...

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“…Fig.1 shows the decrease of the viscosity coefficient with the increase of strain ǫ. In order to compare the hereby predicted effects with the available data based on a hydrodynamic approach [6][7][8], let us introduce the so-called kinematic viscosity ν which is related to the shear coefficient via the mass density ρ of the fluid as follows, ν = η/ρ. According to [8], at room temperature the mass density of electronic fluid in graphene is of the order of ρ ≃ 6 × 10 −19 kg/m 2 leading to ν(0) ≃ 0.005m 2 /s.…”

Section: Resultsmentioning

confidence: 99%

On the electronic viscosity of a Dirac fluid in deformed graphene

Sergeenkov

Ausloos²

2016

Philosophical Magazine Letters

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We discuss the properties of the electronic viscosity of a Dirac fluid in deformed graphene by introducing a strain ǫ and a velocity gradient ∇v, as equivalent to a pseudo-magnetic B d ∝ ǫ and a pseudo-electric E d ∝ ∇v field respectively into the Dirac equation. It is thereby analytically established that the dynamic shear viscosity coefficient η substantially decreases with the applied strain as η(ǫ) = η(0)(1 + 2ǫ) −3/2 , reaching as much as [η(0) − η(ǫ)]/η(0) ≃ 70% for ǫ = 0.5.

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Preturbulent Regimes in Graphene Flow

Cited by 88 publications

References 17 publications

Gaussian quadrature and lattice discretization of the Fermi-Dirac distribution for graphene

Gaussian quadrature and lattice discretization of the Fermi-Dirac distribution for graphene

Fully relativistic lattice Boltzmann algorithm

On the electronic viscosity of a Dirac fluid in deformed graphene

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