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The lattice Boltzmann method has become a standard technique for simulating a wide range of fluid flows. However, the intrinsic coupling of momentum and space discretization restricts the traditional lattice Boltzmann method to regular…

Since its origins, lattice-Boltzmann methods have been restricted to rectangular coordinates, a fact which jeopardises the applications to problems with cylindrical or spherical symmetries and complicates the implementations with complex…

We systematically derived hydrodynamic equations and transport coefficients for a class of multi-speed lattice Boltzmann models in D dimensions, using the multi-scale technique. The constitutive relation of physical fluid is recovered by a…

We demonstrate that lattice QCD calculations can be made $10^3$--$10^6$ times faster by using very coarse lattices. To obtain accurate results, we replace the standard lattice actions by perturbatively-improved actions with tadpole-improved…

We perturb with an additive Gaussian white noise the Hamiltonian system associated to a cubic anharmonic oscillator. The stochastic system is assumed to start from initial conditions that guarantee the existence of a periodic solution for…

We extend a theory of first order hbar corrections to Gutzwiller's trace formula for systems with a smooth potential to systems with discrete symmetries and, as an example, apply the method to the two-dimensional hydrogen atom in a uniform…

We explore the Carlemann 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…

We analyze the properties of a class of improved lattice topological charge density operators, constructed by a smearing-like procedure. By optimizing the choice of the parameters introduced in their definition, we find operators having (i)…

We present a novel method to determine on the lattice both the real and imaginary parts of complex electroweak amplitudes involving two external currents and a single hadron or the QCD vacuum in the external states. The method is based on…

We point out an equivalence between the discrete velocity method of solving the Boltzmann equation, of which the lattice Boltzmann equation method is a special example, and the approximations to the Boltzmann equation by a Hermite…

The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator is developed. Based upon the $\hbar$-expansions and suitable quantization conditions a new…

We derive the partial differential equation (PDE) to which the pseudo-potential lattice Boltzmann method (P-LBM) converges under diffusive scaling, providing a rigorous basis for its consistency analysis. By establishing a direct link…

A unified framework to derive discrete time-marching schemes for coupling of immersed solid and elastic objects to the lattice Boltzmann method is presented. Based on operator splitting for the discrete Boltzmann equation, second-order…

Lattice Boltzmann methods are numerical schemes derived as a kinetic approximation of an underlying lattice gas. A numerical convergence theory for nonlinear convective-diffusive lattice Boltzmann methods is established. Convergence,…

We discuss a discrete approach to the multiscale reductive perturbative method and apply it to a biatomic chain with a nonlinear interaction between the atoms. This system is important to describe the time evolution of localized solitonic…

Convergence properties of Taylor expansions of observables, which are also used in lattice QCD calculations at non-zero chemical potential, are analyzed in an effective N_f = 2+1 flavor Polyakov-quark-meson model. A recently developed…

Lattice Boltzmann simulations have been very successful in simulating liquid-gas and other multi-phase fluid systems. However, the underlying second order analysis of the equation of motion has long been known to be insufficient to…

In this contribution, we address the numerical solutions of high-order asymptotic equivalent partial differential equations with the results of a lattice Boltzmann scheme for an inhomogeneous advection problem in one spatial dimension. We…

We obtain the quadratic term in Euler's asymptotic expansion of the nth harmonic number by a simple modification of Young's elementary determination of the linear term.

The Allen-Cahn equation (ACE) inherently possesses two crucial properties: the maximum principle and the energy dissipation law. Preserving these two properties at the discrete level is also necessary in the numerical methods for the ACE.…