Rotational invariance in the three-dimensional lattice Boltzmann method is dependent on the choice of lattice

The lattice Boltzmann method has recently gained popularity as a tool for simulating complex fluid flows. It uses discrete sets of velocity vectors, or lattices, to create a reduced model of the molecular dynamics of a continuum fluid. While several lattices are believed to behave isotropically, there are reports of qualitatively incorrect results. However, thus far, the reason as to why a lack of isotropy occurs is not known. Based on the hypothesis that lower order lattices may not display rotational invariance, this study tests the isotropy of the D3Q15, D3Q19 and D3Q27 lattices by performing simulations at intermediate Reynolds numbers (50–500) and low Knudsen number (<0.0005) in an axisymmetrical geometry with a nozzle leading to a throat followed by a sudden expansion. The symmetry properties of the results were examined. It was found that at Re ? 250 the D3Q15 and D3Q19 lattices produced different results depending on the plane of the lattice with which the flow was aligned. Lattice planes with fewer than six velocity vectors consistently produced results which were qualitatively different from the planes with six or more velocity vectors. These errors were not observed at Re = 50 or when a D3Q27 lattice was used. They appeared to be independent of grid density, collision operator and Ma. This suggests that the lattices which contain these planes are not fully isotropic and therefore do not properly replicate the behavior of a real fluid in this particular situation, notably downstream from the expansion. Predictions made using these models in more complex geometries may therefore be affected by the orientation of the lattice. When using LBM in CFD simulation (including validation) this study highlights the need for caution to ensure that the solution obtained is independent of the lattice orientation throughout the domain.     

EFFECTIVE DYNAMICS OF A COUPLED MICROSCOPIC-MACROSCOPIC STOCHASTIC SYSTEM

A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the effective system is shown to approximate the original system, in the sense of a probabilistic convergence.     

Adsorption of a single polymer chain on a surface: A molecular dynamics simulation study

We performed simulations of the physical adsorption of a single globular chain on a surface of hemispherical shape by means of molecular dynamics simulations. For the chain, we took advantage of a united atom model. Interactions within the chain were limited to stretching, bending, and torsional as well as nonbonded interactions between the nonadjacent atoms. The interaction between each chain element and the surface formation are reigned by a Lennard–Jones potential. In this article, we focused on differences in the behavior of the adsorbed globule to the free unadsorbed one particularly in two different zones of the immediate vicinity of the surface. There were strong indications for a localized acceleration of the dynamics as compared with the bulk that appears in an increase of trans–gauche switches. For explanation we came up with an adsorption scenario. Special attention was given to the shift of the percentage of trans and gauche conformations within the globule in dependence on the strength of the adsorption potential that might be related to crystallization or glass transition. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2333–2339, 2001     

String dynamics near a black hole

The dynamics of a string near a Kaluza-Klein black hole are studied. Solutions to the geodesic equations are obtained using the world sheet velocity of light as an expansion parameter. For a string falling into a magnetically charged black hole, it is shown that the compact dimension decreases with the world-sheet coordinate τ.     

Vortex core physics in the cuprate superconductor Nd2−xCexCuOy

Flux-flow voltage steps and negative differential resistivity in the cuprate Nd_2−xCe_xCuO_y are explained in terms of subbands between the Fermi energy and the energy gap affecting the quasiparticle dynamics.     

Effect of aromatic substitution on phase behavior of blends of halogenated polystyrene and conventional polystyrene

Miscibility phase behavior in blends of poly(bromostyrene) with polystyrene (PS) has been investigated by means of time‐resolved light scattering, optical microscopy, and DSC. Cloud point phase diagrams of blends of conventional PS with poly‐(2‐bromostyrene) (P2BrS), poly‐(3‐bromostyrene), and poly‐(4‐bromostyrene) of comparable molecular weights were established by light scattering. Of particular interest is the fact that ortho, meta, and para substitutions in the styrenic aromatic rings of poly(bromostyrene) show profound effects on the composition–temperature phase diagrams of their blends with PS, exhibiting a lower critical‐solution temperature (LCST), an upper critical solution temperature (UCST), and combined LCST/UCST diagrams, respectively. Poly‐(2‐chlorostyrene) exhibits an LCST behavior very close to that of the P2BrS blend, suggesting that these types of halogen atoms may be inconsequential to phase behavior. A similar study has been extended to a PS blend containing commercial brominated PS (66 mol % bromine substitution) to determine what location of bromine substitution is crucial for miscibility enhancement in the flame‐retardant brominated PS blends. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1605–1615, 2001     

Flexible host frameworks with diverse cavities in inclusion crystals of bile acids and their derivatives

We have systematically investigated structures and properties of inclusion crystals of bile acids and their derivatives. These steroidal compounds form diverse host frameworks having zero‐, one‐ and two‐dimensional cavities, causing various inclusion behaviors towards many organic compounds. The diverse host frameworks exhibit the following guest‐dependent flexibility. First, the frameworks mainly depend on the included guests in size and shape. The size‐dependence is quantitatively estimated by the parameter PCcavity, which is the volume ratio of a guest molecule to a host cavity. The resulting values of PCcavity lie in the range of 42–76%. Second, each of the host frameworks has its own range of the values. Some guests can employ two different frameworks with the boundary values, explaining formation of polymorphic crystals. Third, the host frameworks are selected by host–guest interactions through weak hydrogen bonds, such as NH/π and CH/O. The weak hydrogen bonds play an important role for various selective inclusion processes. Fourth, the host frameworks are dynamically exchangeable, resulting in intercalation and polymerization in the cavities. These static and dynamic structures of the frameworks demonstrate great potential of crystalline organic inclusion compounds as functional materials. © 2009 The Japan Chemical Journal Forum and Wiley Periodicals, Inc. Chem Rec 9: 124–135; 2009: Published online in Wiley InterScience ( www.interscience.wiley.com ) DOI 10.1002/tcr.20171     

Reargument over E ～ j relation of high temperature superconductors

The E ∼ j relation of an HTSC slab is solved strictly within the Bean’s model in two different situations where the system does and does not reach equilibrium state under the magnetic relaxation respectively, with both forward and backward hopping taken into consideration (the backward hopping means the hopping from the barriers with low energy to high ones). Our results suggest and rigorously prove that the In E ∼ In j curves show only positive curvature on the side of slab where the directions of current-created field and the applied field are the same, while they show both positive and negative curvatures at a certain field range on the other side where the directions are opposite. The relationship of the positive and negative curvatures with the critical current, applied field and temperature is also discussed.     

MULTIAXIAL BEHAVIOR OF NANOPOROUS SINGLE CRYSTAL COPPER： A MOLECULAR DYNAMICS STUDY

The stress-strain behavior and copper are studied by the molecular dynamics incipient yield surface of nanoporous single crystal （MD） method. The problem is modeled by a periodic unit cell subject to multi-axial loading. The loading induced defect evolution is explored. The incipient yield surfaces are found to be tension-compression asymmetric. For a given void volume fraction, apparent size effects in the yield surface are predicted： the smaller behaves stronger. The evolution pattern of defects （i.e., dislocation and stacking faults） is insensitive to the model size and void volume fraction. However, it is loading path dependent. Squared prismatic dislocation loops dominate the incipient yielding under hydrostatic tension while stacking-faults are the primary defects for hydrostatic compression and uniaxial tension/compression.