Variational solution to the lattice Boltzmann method for Couette flow.

Literature studies of the lattice Boltzmann method (LBM) demonstrate hydrodynamics beyond the continuum limit. This includes exact analytical solutions to the LBM, for the bulk velocity and shear stress of Couette flow under diffuse reflection at the walls through the solution of equivalent moment equations. We prove that the bulk velocity and shear stress of Couette flow with Maxwell-type boundary conditions at the walls, as specified by two-dimensional isothermal lattice Boltzmann models, are inherently linear in Mach number. Our finding enables a systematic variational approach to be formulated that exhibits superior computational efficiency than the previously reported moment method. Specifically, the number of partial differential equations (PDEs) in the variational method grows linearly with quadrature order while the number of moment method PDEs grows quadratically. The variational method directly yields a system of linear PDEs that provide exact analytical solutions to the LBM bulk velocity field and shear stress for Couette flow with Maxwell-type boundary conditions. It is anticipated that this variational approach will find utility in calculating analytical solutions for novel lattice Boltzmann quadrature schemes and other flows.

Staggered scheme for the compressible fluctuating hydrodynamics of multispecies fluid mixtures.

We present a numerical formulation for the solution of nonisothermal, compressible Navier-Stokes equations with thermal fluctuations to describe mesoscale transport phenomena in multispecies fluid mixtures. The novelty of our numerical method is the use of staggered grid momenta along with a finite volume discretization of the thermodynamic variables to solve the resulting stochastic partial differential equations. The key advantages of the numerical scheme are that it significantly simplifies the discretization of diffusive and stochastic momentum fluxes into a more compact form, and it provides an unambiguous prescription of boundary conditions involving pressure. The staggered grid scheme more accurately reproduces the equilibrium static structure factor of hydrodynamic fluctuations in gas mixtures compared to a collocated scheme described previously by Balakrishnan et al. [Phys. Rev. E 89, 013017 (2014)1539-375510.1103/PhysRevE.89.013017]. The numerical method is tested for ideal noble gases mixtures under various nonequilibrium conditions, such as applied thermal and concentration gradients, to assess the role of cross-diffusion effects, such as Soret and Dufour, on the long-ranged correlations of hydrodynamic fluctuations, which are also more accurately reproduced compared to the collocated scheme. We numerically study giant nonequilibrium fluctuations driven by concentration gradients and fluctuation-driven Rayleigh-Taylor instability in gas mixtures. Wherever applicable, excellent agreement is observed with theory and measurements from the direct simulation Monte Carlo method.

Squeeze-Film Effect on Atomically Thin Resonators in the High-Pressure Limit.

The resonance frequency of membranes depends on the gas pressure due to the squeeze-film effect, induced by the compression of a thin gas film that is trapped underneath the resonator by the high-frequency motion. This effect is particularly large in low-mass graphene membranes, which makes them promising candidates for pressure-sensing applications. Here, we study the squeeze-film effect in single-layer graphene resonators and find that their resonance frequency is lower than expected from models assuming ideal compression. To understand this deviation, we perform Boltzmann and continuum finite-element simulations and propose an improved model that includes the effects of gas leakage and can account for the observed pressure dependence of the resonance frequency. Thus, this work provides further understanding of the squeeze-film effect and provides further directions into optimizing the design of squeeze-film pressure sensors from 2D materials.

Origin of spurious oscillations in lattice Boltzmann simulations of oscillatory noncontinuum gas flows.

Oscillatory noncontinuum gas flows at the micro and nanoscales are characterized by two dimensionless groups: a dimensionless molecular length scale, the Knudsen number Kn, and a dimensionless frequency θ, relating the oscillatory frequency to the molecular collision frequency. In a recent study [Shi et al., Phys. Rev. E 89, 033305 (2014)10.1103/PhysRevE.89.033305], the accuracy of the lattice Boltzmann (LB) method for simulating these flows at moderate-to-large Kn and θ was examined. In these cases, the LB method exhibits spurious numerical oscillations that cannot be removed through the use of discrete particle velocities drawn from higher-order Gauss-Hermite quadrature. Here, we identify the origin of these spurious effects and formulate a method to minimize their presence. This proposed method splits the linearized Boltzmann Bhatnagar-Gross-Krook (BGK) equation into two equations: (1) a homogeneous "gain-free equation" that can be solved directly, containing terms responsible for the spurious oscillations; and (2) an inhomogeneous "remainder equation" with homogeneous boundary conditions (i.e., stationary boundaries) that is solved using the conventional LB algorithm. This proposed "splitting method" is validated using published high-accuracy numerical solutions to the linearized Boltzmann BGK equation where excellent agreement is observed.

Further increase in thermostability of Moloney murine leukemia virus reverse transcriptase by mutational combination.

We previously generated a highly thermostable triple variant of Moloney murine leukemia virus reverse transcriptase, MM3 (E286R/E302K/L435R), by introducing positive charges by site-directed mutagenesis at positions that have been implicated in the interaction with template-primer (Yasukawa et al., (2010) J. Biotechnol., 150, 299-306). In this study, we attempted to further increase the thermostability of MM3. Twenty-nine mutations were newly designed, focusing on the number of surface charge, stabilization of hydrophobic core, and introduction of salt bridge. The corresponding 29 single variants were produced in Escherichia coli and characterized for activity and stability. Six mutations (A32V, L41D, L72R, I212R, L272E and W388R) were selected as the candidates for further stabilize MM3. Fifteen multiple variants were designed by combining two or more of the six mutations with the MM3 mutations, produced and characterized. The sextuple variant MM3.14 (A32V/L72R/E286R/E302K/W388R/L435R) exhibited higher thermostability than MM3.