Moment-based formulation of Navier–Maxwell slip boundary conditions for lattice Boltzmann simulations of rarefied flows in microchannels

We present an implementation of first-order Navier–Maxwell slip boundary conditions for simulating near-continuum rarefied flows in microchannels with the lattice Boltzmann method. Rather than imposing boundary conditions directly on the particle velocity distribution functions, following the existing discrete analogs of the specular and diffuse reflection conditions from continuous kinetic theory, we use a moment-based method to impose the Navier–Maxwell slip boundary conditions that relate the velocity and the strain rate at the boundary. We use these conditions to solve for the unknown distribution functions that propagate into the\ud domain across the boundary. We achieve second-order accuracy by reformulating these conditions for the second set of distribution functions that arise in the derivation of the lattice Boltzmann method by an integration along characteristics. The results are in excellent agreement with asymptotic solutions of the compressible Navier-Stokes equations for microchannel flows in the slip regime. Our moment formalism is also valuable for analysing the existing boundary conditions, and explains the origin of numerical slip in the bounce-back and other common boundary conditions that impose explicit conditions on the higher moments instead of on the local tangential velocity

A random projection method for sharp phase boundaries in lattice Boltzmann simulations

Existing lattice Boltzmann models that have been designed to recover a macroscopic description of immiscible liquids are only able to make predictions that are quantitatively correct when the interface that exists between the fluids is smeared over several nodal points. Attempts to minimise the thickness of this interface generally leads to a phenomenon known as lattice pinning, the precise cause of which is not well understood. This spurious behaviour is remarkably similar to that associated with the numerical simulation of hyperbolic partial differential equations coupled with a stiff source term. Inspired by the seminal work in this field, we derive a lattice Boltzmann implementation of a model equation used to investigate such peculiarities. This implementation is extended to different spacial discretisations in one and two dimensions. We shown that the inclusion of a quasi-random threshold dramatically delays the onset of pinning and facetting

A NOTE ON COMONOTONICITY AND POSITIVITY OF THE CONTROL COMPONENTS OF DECOUPLED QUADRATIC FBSDE

In this small note we are concerned with the solution of Forward-Backward Stochastic Differential Equations (FBSDE) with drivers that grow quadratically in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem is a comparison result that allows comparing componentwise the signs of the control processes of two different qgFBSDE. As a byproduct one obtains conditions that allow establishing the positivity of the control process.Comment: accepted for publicatio

Quantum evolution of scalar fields in Robertson-Walker space-time

We study the $\lambda \phi^4$ field theory in a flat Robertson-Walker space-time using the functional Sch\"odinger picture. We introduce a simple Gaussian approximation to analyze the time evolution of pure states and we establish the renormalizability of the approximation. We also show that the energy-momentum tensor in this approximation is finite once we consider the usual mass and coupling constant renormalizations.Comment: Revtex file, 19 pages, no figures. Compressed ps version available at http://phenom.physics.wisc.edu/pub/preprints/1995/madph-95-912.ps.Z or at ftp://phenom.physics.wisc.edu/pub/preprints/1995/madph-95-912.ps.

Phases of granular segregation in a binary mixture

We present results from an extensive experimental investigation into granular segregation of a shallow binary mixture in which particles are driven by frictional interactions with the surface of a vibrating horizontal tray. Three distinct phases of the mixture are established viz; binary gas (unsegregated), segregation liquid and segregation crystal. Their ranges of existence are mapped out as a function of the system's primary control parameters using a number of measures based on Voronoi tessellation. We study the associated transitions and show that segregation can be suppressed is the total filling fraction of the granular layer, $C$, is decreased below a critical value, $C_{c}$, or if the dimensionless acceleration of the driving, $\gamma$, is increased above a value $\gamma_{c}$.Comment: 12 pages, 12 figures, submitted to Phys. Rev.

Vibrational spectroscopic force field studies of dimethyl sulfoxide and hexakis(dimethyl sulfoxide)scandium(III) iodide, and crystal and solution structure of the hexakis(dimethyl sulfoxide)scandium(III) ion

Hexakis(dimethyl sulfoxide) scandium(III) iodide, [Sc(OS(CH3)(2))(6)]I-3 contains centrosymmetric hexasolvated scandium(III) ions with an Sc-O bond distance of 2.069(3) Angstrom. EXAFS spectra yield a mean Sc-O bond distance of 2.09(1) Angstrom for solvated scandium(III) ions in dimethyl sulfoxide solution, consistent with six-coordination. Raman and infrared absorption spectra have been recorded, also of the deuterated compound, and analysed by means of normal coordinate methods, together with spectra of dimethyl sulfoxide. The effects on the vibrational spectra of the weak intermolecular C-H...O interactions and of the dipole dipole interactions in liquid dimethyl sulfoxide have been evaluated, in particular for the S O stretching mode. The strong Raman band at 1043.6 cm(-1) and the intense IR absorption at 1062.6 cm(-1) have been assigned as the S-O stretching frequencies of the dominating species in liquid dimethyl sulfoxide, evaluated as centrosymmetric dimers with antiparallel polar S-O groups. The shifts of vibrational frequencies and force constants for coordinated dimethyl sulfoxide ligands in hexasolvated trivalent metal ion complexes are discussed. Hexasolvated scandium( III) ions are found in dimethyl sulfoxide solution and in [Sc(OSMe2)(6)]I-3. The iodide ion dipole attraction shifts the methyl group C H stretching frequency for (S-)C-H...I- more than for the intermolecular (S-)C-H...O interactions in liquid dimethyl sulfoxide