Analysis of Carleman Linearization of Lattice Boltzmann

We explore the Carleman linearization of the collision term of the lattice Boltzmann formulation, as a first step towards formulating a quantum lattice Boltzmann algorithm. Specifically, we deal with the case of a single, incompressible fluid with the Bhatnagar Gross and Krook equilibrium function. Under this assumption, the error in the velocities is proportional to the square of the Mach number. Then, we showcase the Carleman linearization technique for the system under study. We compute an upper bound to the number of variables as a function of the order of the Carleman linearization. We study both collision and streaming steps of the lattice Boltzmann formulation under Carleman linearization. We analytically show why linearizing the collision step sacrifices the exactness of streaming in lattice Boltzmann, while also contributing to the blow up in the number of Carleman variables in the classical algorithm. The error arising from Carleman linearization has been shown analytically and numerically to improve exponentially with the Carleman linearization order. This bodes well for the development of a corresponding quantum computing algorithm based on the Lattice Boltzmann equation.

Investigation of dimensional accuracy of metal droplet deposition under repulsion using a lattice Boltzmann approach

Purpose This paper aims to investigate the influence of droplet infiltration and sliding on the deposition size and make a uniform deposition by controlling the interaction between droplets, using the three-dimensional lattice Boltzmann method (LBM) based on the actual working condition. Design/methodology/approach D3Q19 Shan-Chen LB approach is developed and optimized based on the metal droplet deposition. The Carnahan-Starling equation of state and transition layers are introduced to maintain the greater stability and low pseudo velocities. In addition, an additional collision term is adopted to implement immersed moving boundary scheme to deal with no-slip boundaries on the front of the phase change. Findings The numerical results show that the new¬ incoming droplet wet and slide off the solidified surface and the rejection between droplets are the reasons for the deviation of the actual deposition length. The total length of the longitudinal section negatively correlates with the deposition distance. To improve the dimensional accuracy, the deposition distance and repulsion rate need to be guaranteed. The optimal deposition distance is found to have a negative linear correlation with wettability. Originality/value The numerical model developed in this paper will help predict the continuous metal droplet deposition and provide guidance for the selection of deposition distance.

Neutrino non-standard interactions meet precision measurements of Neff

The number of relativistic species, Neff, has been precisely calculated in the standard model, and would be measured to the percent level by CMB-S4 in future. Neutral-current non-standard interactions would affect neutrino decoupling in the early Universe, thus modifying Neff. We parameterize those operators up to dimension-7 in the effective field theory framework, and then provide a complete, generic and analytical dictionary for the collision term integrals. From precision measurements of Neff, the most stringent constraint is obtained for the dimension-6 vector-type neutrino-electron operator, whose scale is constrained to be above about 195 (331) GeV from Planck (CMB-S4). We find our results complementary to other experiments like neutrino coherent scattering, neutrino oscillation, collider, and neutrino deep inelastic scattering experiments.

Wigner functions and quantum kinetic theory of polarized photons

We derive the Wigner functions of polarized photons in the Coulomb gauge with the ħ expansion applied to quantum field theory, and identify side-jump effects for massless photons. We also discuss the photonic chiral vortical effect for the Chern-Simons current and zilch vortical effect for the zilch current in local thermal equilibrium as a consistency check for our formalism. The results are found to be in agreement with those obtained from different approaches. Moreover, using the real-time formalism, we construct the quantum kinetic theory (QKT) for polarized photons. By further adopting a specific power counting scheme for the distribution functions, we provide a more succinct form of an effective QKT. This photonic QKT involves quantum corrections associated with self-energy gradients in the collision term, which are analogous to the side-jump corrections pertinent to spin-orbit interactions in the chiral kinetic theory for massless fermions. The same theoretical framework can also be directly applied to weakly coupled gluons in the absence of background color fields.

Lattice Boltzmann Modelling for Natural Convection in Power-Law Fluids within a Partially Heated Square Enclosure

The present paper reports the numerical investigations for steady-state natural convection in power-law fluids inside a square enclosure embedded with bottom discrete heaters. The Lattice Boltzmann Method (LBM) is employed to model the flow and heat transfer phenomenon at different combinations of power-law index, Rayleigh number, and heat source length for a constant Prandtl number. The buoyancy force is incorporated in the collision term of the LBM through Boussinesq approximation. Simulation outcomes are furnished using streamlines and, temperature contours, velocity profiles and variation of heat transfer on the non-adiabatic walls to probe natural convection phenomena. The results indicate that the temperature and the flow fields in the enclosure are symmetric about the vertical centerline. The detailed physical interpretations have been provided for the reported results. Further, the increase in the power-law index means a rise in viscosity and a decrease in thermal energy transport for other constant parameters. The outcomes also specify that the intensity of circulation and heat transfer enhances with the increase of Rayleigh number and size of the localized heater. Finally, though, a rise in the size of the confined heat source enhances the rate of total thermal transport, it does not change the trend of fluid flow and local heat transfer rate.

On the Theory of Determining the Transport Characteristics of Gas Mixtures

The paper considers the identification of properties of real gases and creation of nanomaterials on the basis of molecular and kinetic theory of gases, namely the Boltzmann equation. The collision term of the Boltzmann equation is used in the algorithm for the identification of transport properties of media. The article analyses the uniform convergence of improper integrals in the collision term of the Boltzmann equation depending on the conditions for the connection between the kinetic and potential energy of interacting molecules. This analysis allows to soundly identify the transport coefficient in macro equations of heat and mass transfer.

A Parallel Image Registration Algorithm Based on a Lattice Boltzmann Model

Image registration is a key pre-procedure for high level image processing. However, taking into consideration the complexity and accuracy of the algorithm, the image registration algorithm always has high time complexity. To speed up the registration algorithm, parallel computation is a relevant strategy. Parallelizing the algorithm by implementing Lattice Boltzmann method (LBM) seems a good candidate. In consequence, this paper proposes a novel parallel LBM based model (LB model) for image registration. The main idea of our method consists in simulating the convection diffusion equation through a LB model with an ad hoc collision term. By applying our method on computed tomography angiography images (CTA images), Magnet Resonance images (MR images), natural scene image and artificial images, our model proves to be faster than classical methods and achieves accurate registration. In the continuity of 2D image registration model, the LB model is extended to 3D volume registration providing excellent results in domain such as medical imaging. Our method can run on massively parallel architectures, ranging from embedded field programmable gate arrays (FPGAs) and digital signal processors (DSPs) up to graphics processing units (GPUs).

Isospin Effects on Subthreshold Particle Production

The production/absorption rate of particles in compressed and heated asymmetric matter is studied using a Relativistic Mean Field (RMF) transport model with an isospin dependent collision term. We show that the K+/K° ratio reflects the isospin effects on the production rates just because of the large sensitivity around the threshold. The results are very promising with respect to the possibility of a direct link between particle production data in exotic Heavy Ion Collisions (HIC) and the isospin dependent part of the Equation of State (EoS) at high baryon densities.