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

A volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations

Lattice Boltzmann models that recover a macroscopic description of multiphase flow of immiscible liquids typically represent the boundaries between phases using a scalar function, the phase field, that varies smoothly over several grid points. Attempts to tune the model parameters to minimise the thicknesses of these interfaces typically lead to the interfaces becoming fixed to the underlying grid instead of advecting with the fluid velocity. This phenomenon, known as lattice pinning, is strikingly similar to that associated with the numerical simulation of conservation laws coupled to stiff algebraic source terms. We present a lattice Boltzmann formulation of the model problem proposed by LeVeque and Yee [J. Comput. Phys. 86, 187] to study the latter phenomenon in the context of computational combustion, and offer a volume-conserving extension in multiple space dimensions. Inspired by the random projection method of Bao and Jin [J. Comput. Phys. 163, 216] we further generalise this formulation by introducing a uniformly distributed quasi-random variable into the term responsible for the sharpening of phase boundaries. This method is mass conserving and the statistical average of this method is shown to significantly delay the onset of pinning

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.

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

Observational Constraints on Silent Quartessence

We derive new constraints set by SNIa experiments (`gold' data sample of Riess et al.), X-ray galaxy cluster data (Allen et al. Chandra measurements of the X-ray gas mass fraction in 26 clusters), large scale structure (Sloan Digital Sky Survey spectrum) and cosmic microwave background (WMAP) on the quartessence Chaplygin model. We consider both adiabatic perturbations and intrinsic non-adiabatic perturbations such that the effective sound speed vanishes (Silent Chaplygin). We show that for the adiabatic case, only models with equation of state parameter $|\alpha |\lesssim 10^{-2}$ are allowed: this means that the allowed models are very close to \LambdaCDM. In the Silent case, however, the results are consistent with observations in a much broader range, -0.3<\alpha<0.7.Comment: 7 pages, 12 figures, to be submitted to JCA

Raquialgias na Criança

As raquialgias são, na criança e no adolescente, menos frequentes do que no adulto, mas traduzem, com maior frequência, a existência de patologia subjacente. Longe de constituírem um gasto excessivo de tempo do clínico, a colheita minuciosa da história clínica e um exame objectivo cuidadoso e sistemático são, indubitavelmente, um dos melhores investimentos do médico que vê crianças com este tipo de sintoma. Permitem abordar correctamente o doente e a sua doença e a solicitação dos exames complementares de diagnóstico mais adequados, em face de uma hipótese diagnóstica correctamente equacionada. Perante uma criança com raquialgias, a atitude depende da idade, da gravidade dos sinais encontrados na observação e da existência de complicações neurológicas ou outros sinais extra-raquidianos; na sua ausência, é prudente seguir a evolução das queixas durante algum tempo, antes de submeter o doente a uma investigação frequentemente onerosa, consumidora de tempo e com baixa probabilidade de êxito