Min Soe

Superfluid Turbulence from Quantum Kelvin Wave to Classical Kolmogorov Cascades

The main topological feature of a superfluid is a quantum vortex with an identifiable inner and outer radius. A novel unitary quantum lattice gas algorithm is used to simulate quantum turbulence of a Bose-Einstein condensate superfluid described by the Gross-Pitaevskii equation on grids up to 5760(3). For the first time, an accurate power-law scaling for the quantum Kelvin wave cascade is determined: k(-3). The incompressible kinetic energy spectrum exhibits very distinct power-law spectra in 3 ranges of k space: a classical Kolmogorov k(-(5/3)) spectrum at scales greater than the outer radius of individual quantum vortex cores and a quantum Kelvin wave cascade spectrum k(-3) on scales smaller than the inner radius of the quantum vortex core. The k(-3) quantum Kelvin wave spectrum due to phonon radiation is robust, while the k(-(5/3)) classical Kolmogorov spectrum becomes robust on large grids.

Magnetic field stabilization of a two-dimensional fluid jet: a multiple relaxation Lattice Boltzmann simulation

The stabilization of a two-dimensional fluid jet from the Kelvin–Helmholtz (KH) instability by an external parallel magnetic field is examined by lattice Boltzmann techniques. For sufficiently strong magnetic fields, the jet does not break up into large-scale vortices but retains the major features of the jet, albeit somewhat expanded. There are time-dependent striations within the expanded jet.

A 9-bit multiple relaxation Lattice Boltzmann magnetohydrodynamic algorithm for 2D turbulence

While a minimalist representation of 2D Magnetohydrodynamics (MHD) on a square lattice is a 9-bit scalar and 5-bit vector distribution functions, here we examine the effect of using the 9-bit vector distribution function on the effect of a magnetic field on the Kelvin-Helmholtz instability. While there is little difference in the simulation results between the 5-bit and the 9-bit vector distribution models in the vorticity, energy spectra, etc., the 9-bit model permits simulations with mean magnetic field a factor of approximately 2 greater than those attainable in the standard 5-bit model. Indeed a 9-bit single-relaxation model can attain such success over a 5-bit multiple-relaxation model at the same computational expense.

Unitary quantum lattice gas algorithm generated from the Dirac collision operator for 1D soliton–soliton collisions

A new unitary quantum lattice gas (QLG) algorithm is proposed as a mesoscopic unitary perturbative representation of the mean field Gross Pitaevskii equation for Bose–Einstein Condensates (BECs). This consists of an interleaved sequence of unitary collide-stream operators and is tested on the 1D nonlinear Schrödinger (NLS) equation since exact soliton solutions are well known. An earlier QLG algorithm, based on the collision operator has been found to have limited application to spinor-BECs. Here, a new unitary collision operator, based on the recent QLG of Yepez for the Dirac particle, is used to model the 1D NLS soliton–soliton problem. It is found that this new unitary algorithm can handle parameters (soliton amplitudes and speeds) a factor of over 20 greater than those under the previous algorithm.[Re: (v.07) To be submitted to special issue ‘Plasma and Fluid Dynamics: Computational, Experimental and Theoretical Advancement’]

Unitary qubit lattice simulations of multiscale phenomena in quantum turbulence

A unitary qubit lattice algorithm, which scales almost perfectly to the full number of cores available (e.g., 216000 cores on a CRAY XT5), is used to examine quantum turbulence and its interrelationship to classical turbulence with production runs on grids up to 57603. The maximal grids achievable by conventional CFD for quantum turbulence is just 20483, and artificial dissipation had to be introduced. Our unitary algorithms preserve the Hamiltonian structure of the Gross-Pitaevskii equation which describes quantum turbulence in a zero-temperature Bose-Einstein condensate (BEC). As a result, parameter regimes have been uncovered which exhibit very short Poincare recurrence time, as well as a strong triple cascade structure in the kinetic energy spectrum. Moreover, a detailed examination of the incompressible kinetic energy spectrum has revealed for the first time within a turbulence simulation the k-17/5 quantum Kelvin wave cascade. By generalizing the unitary entanglement operators on the 2 qubits, a finite temperature BEC system is examined. These unitary qubit lattice algorithms are directly applicable to quantum computers as they become available.

Lattice Boltzmann algorithms for plasma physics

Lattice Boltzmann (LB) algorithms are a mesoscopic approach to the solution of nonlinear macroscopic physics, which can be ideally parallelized on supercomputers to the full number of cores available. This is in contrast to the standard direct solution of the nonlinear physics by computational fluid dynamics codes. In its original formulation, LB algorithm consisted of a split operator method: collision relaxation at a spatial node, followed by appropriate streaming of the post-collision distribution to neighboring lattice sites. To reduce memory constraints, a minimal number of lattice streaming vectors are permitted so that one recovers the given nonlinear physics equations in the Chapman-Enskog limit. As in kinetic theory, the macroscopic transport coefficients are determined by the collisional relaxation time in the LB equation. The algorithm is explicit and typically is second-order accurate. However, the simple LB algorithm is prone to numerical instabilities for high Reynolds number flows. In this paper we review some of the recent attempts at stabilizing the LB algorithm for fluid flows – in particular multiple-relaxation operators, introduction of quasi-equiibria states as well as entropic methods. These methods are then discussed in reference to the LB representation of resistive magnetohydrodynamics. The introduction of a vector distribution function for the magnetic field permits the exact satisfaction of the zero divergence of the magnetic field. As a final example, the LB representation of Landau damping is reviewed.

Benchmarking the Dirac-generated unitary lattice qubit collision-stream algorithm for 1D vector Manakov soliton collisions

The unitary quantum lattice gas (QLG) algorithm is a mesoscopic unitary perturbative representation that can model the mean field Gross Pitaevskii equation for the evolution of the ground state wave function of Bose Einstein Condensates (BECs). The QLG considered here consists of an interleaved sequence of unitary collide-stream operators, with the collision operator being deduced from that for the Dirac equation, with the nonlinear potentials of the BECs being the mass term in the Dirac equation. Since the unitary collision operator is more accurate one obtains a more accurate representation of the nonlinear terms. Further benchmark QLG simulations are reported here: that for the exactly soluble 1D vector Manakov soliton collisions. It is found that this Dirac-based unitary algorithm permits simulations with vector soliton parameters (soliton amplitudes and speeds) that are considerably greater than those achieved under our previous swap QLG algorithm.

Poincare recurrence and spectral cascades in three-dimensional quantum turbulence

The evolution of the ground state wave function of a zero-temperature Bose-Einstein condensate (BEC) is well described by the Hamiltonian Gross-Pitaevskii (GP) equation. Using a set of appropriately interleaved unitary collision-streaming operators, a quantum lattice gas algorithm is devised which on taking moments recovers the Gross-Pitaevskii (GP) equation in diffusion ordering (time scales as square of length). Unexpectedly, there is a class of initial conditions in which their Poincare recurrence is extremely short. Further it is shown that the Poincare recurrence time scales with diffusion ordering as the the grid is increased. The spectral results of Yepez et.al. [1] for quantum turbulence are corrected and it is found that it is the compressible kinetic energy spectrum that exhibits the 3 cascade regions: a small k classical Kolmogorov k^(-5/3) spectrum, a steep semi-classical cascade region, and a large k quantum Kelvin wave cascade k^(-3) spectrum. The incompressible kinetic energy spectrum exhibits basically a single cascade power law of k^(-3). For winding number 1 linear vortices it is also shown that there is an intermittent loss of Kelvin wave cascade with its signature seen in the time evolution of the kinetic energy, the loss of the k^(-3) spectrum in the incompressible kinetic energy spectrum as well as the minimization of the vortex core isosurfaces that inhibits the Kelvin wave cascade.

Lattice Boltzmann Algorithms for Fluid Turbulence

Lattice Boltzmann algorihms are a mesoscopic representation of nonlinear continuum physics (like Navier-Stokes, magnetohydro dynamics (MHD), Gross- Pitaevskii equations) which are ideal for parallel supercomputers because they transform the difficult nonlinear convective macroscopic derivatives into purely local moments of distribution functions. The macroscopic nonlinearities are recovered by relaxation distribution functions in the collision operator whose dependence on the macroscopic velocity is algebraically nonlinear and thus purely local. Unlike standard computational fluid dynamics codes, there is no loss in parallelization in handling arbitrary geometric boundaries, e.g., using bounce-back rules from kinetic theory. By encoding detailed balance into the collision operator through the introduction of discrete H-function, the lattice Boltzmann algorithm can be made unconditionally stable for arbitrary high Reynolds numbers. It is shown that this approach is a special case of a quantum lattice Boltzmann algorithm that entangles local qubits through unitary collision operators and which is ideally parallelized on quantum computer architectures. Here we consider turbulence simulations using 2,048 PEs on a 1,6003-spatial grid. A connection is found between the rate of change of enstrophy and the onset of laminar-to- turbulent flows.

Effect of Fourier transform on the streaming in quantum lattice gas algorithms

ABSTRACT All our previous quantum lattice gas algorithms for nonlinear physics have approximated the kinetic energy operator by streaming sequences to neighboring lattice sites. Here, the kinetic energy can be treated to all orders by Fourier transforming the kinetic energy operator with interlaced Dirac-based unitary collision operators. Benchmarking against exact solutions for the 1D nonlinear Schrodinger equation shows an extended range of parameters (soliton speeds and amplitudes) over the Dirac-based near-lattice-site streaming quantum algorithm.