Multiscale spatial Monte Carlo simulations: Multigriding, computational singular perturbation, and hierarchical stochastic closures

A flexible ultraviolet photoconductor based on ZnO and 8-hydroxyquinoline (8HQ) is fabricated. In such a device, the 8HQ film covers the ZnO layer and protects the ZnO from being affected by oxygen via slow adsorption and desorption processes, which would greatly deteriorate the response speed of the device. As a result, the photoconductor exhibits a shorter rise time (10 s) and decay time (27 s) than that of the bare ZnO film based device, in which the times are 133 s and 200 s, respectively. Meanwhile, the device displays a high responsivity of 484 A W−1 under a moderate electric field of 2 × 106 V m−1.

We extended self-consistent field theory to explore self-assembly behavior of linear multiblock copolymers consisting of alternative rod and coil blocks. Such rod-coil multiblock copolymers are found to be capable of self-assembling into hierarchical smectic microstructures. For the copolymers with long rod end block, lamellae-in-lamellar structures containing two smectic C phases at small and large length scales were observed. It was found that the hierarchical smectic structures exhibit not only double periodicities in overall structure but also double orientational orders of rod blocks. Additionally, these hierarchical smectic structures can be tailed by tuning the relative length of the coil blocks. For the copolymers with long coil end block, the multiblock copolymers can self-assemble into hierarchical lamellar structures with smectic phases only at the small length scale. The findings gained through the present study may offer valuable information for understanding the self-assembly behavior of complicated rod-coil copolymers and designing polymeric materials with advanced properties.

Highly efficient adsorption of Pb (II) by Cucurbit[7]uril-modified amino-expanded graphite: Experiments, synthetic modelling optimisation and DFT calculations

Summary Numerical modeling of the in-situ conversion process (ICP) is a challenging endeavor involving thermal multiphase flow, compositional pressure/volume/temperature (PVT) behavior, and chemical reactions that convert solid kerogen into light hydrocarbons, which are tightly coupled to temperature propagation. Our investigations of grid-resolution effects on the accuracy and performance of ICP simulations have demonstrated that ICP-simulation outcomes—specifically, chemical-reaction rates, kerogen-accumulation profiles, and oil-/gas-production rates, may exhibit relatively large errors on coarse grids. Coarse grids are attractive because they deliver favorable computational performance. We have developed a novel multiscale modeling method for simulating ICP that reduces numerical-modeling errors and reproduces fine-scale-simulation results on relatively coarse grids. The method uses a two-scale solution method, in which the reaction kinetics of the solids is solved locally on a fine-scale grid, with interpolated temperatures obtained from coarse-grid simulations of thermal flow and fluid transport. We demonstrate the accuracy and efficiency of our multiscale method with representative 1D models. It is shown that the method delivers accurate solutions for key ICP performance indicators with very little computational overhead compared with corresponding coarse-scale models. The robustness of the multiscale method has been verified over a number of physical-parameter ranges with a limited-scope sensitivity study. Numerical results show that the multiscale method consistently improves the simulation results and matches the fine-scale reference results closely.

Physical theories are developed to describe phenomena in particular regimes, and generally are valid only within a limited range of scales. For example, general relativity provides an effective description of the Universe at large length scales, and has been tested from the cosmic scale down to distances as small as 10 m (Dimopoulos 2007 Phys. Rev. Lett. 98 111102; 2008 Phys. Rev. D 78 042003). In contrast, quantum theory provides an effective description of physics at small length scales. Direct tests of quantum theory have been performed at the smallest probeable scales at the Large Hadron Collider, ∼10−20 m, up to that of hundreds of kilometres (Ursin et al 2007 Nature Phys. 3 481–6). Yet, such tests fall short of the scales required to investigate potentially significant physics that arises at the intersection of quantum and relativistic regimes. We propose to push direct tests of quantum theory to larger and larger length scales, approaching that of the radius of curvature of spacetime, where we begin to probe the interaction between gravity and quantum phenomena. In particular, we review a wide variety of potential tests of fundamental physics that are conceivable with artificial satellites in Earth orbit and elsewhere in the solar system, and attempt to sketch the magnitudes of potentially observable effects. The tests have the potential to determine the applicability of quantum theory at larger length scales, eliminate various alternative physical theories, and place bounds on phenomenological models motivated by ideas about spacetime microstructure from quantum gravity. From a more pragmatic perspective, as quantum communication technologies such as quantum key distribution advance into space towards large distances, some of the fundamental physical effects discussed here may need to be taken into account to make such schemes viable.

In this paper we study the evolution of the kinetic features of the martensitic transition in a Cu-Al-Mn single crystal under thermal cycling. The use of several experimental techniques including optical microscopy, calorimetry, and acoustic emission, has enabled us to perform an analysis at multiple scales. In particular, we have focused on the analysis of avalanche events (associated with the nucleation and growth of martensitic domains), which occur during the transition. There are significant differences between the kinetics at large and small length scales. On the one hand, at small length scales, small avalanche events tend to sum to give new larger events in subsequent loops. On the other hand, at large length scales the large domains tend to split into smaller ones on thermal cycling. We suggest that such different behavior is the necessary ingredient that leads the system to the final critical state corresponding to a power-law distribution of avalanches.

A multi-scale finite-volume (MSFV) method for solving multiphase flow problem in highly heterogeneous media was recently developed. In contrast with classical upscaling techniques, the goal of multiscale methods is not simply to capture the large-scale effects of the fine-scale heterogeneity, but to provide an efficient tool for solving large flow problems with fine-scale resolution. The MSFV is based on a fractional flow formulation of the problem: first an equation for the total velocity is solved, then a fine-scale velocity field is reconstructed, finally the phase-saturation distribution is obtained by solving the nonlinear transport equations. In addition to the original fine grid the MSFV method employs an imposed coarse grid and a dual coarse grid. The first step is to compute the effective parameters that have to be used for solving the global flow problem on a coarse grid. This is done by means of a set of basis functions, which are numerical solutions computed on the cells of the dual grid. From these basis functions, the fluxes across the coarse-block boundaries are computed and the transmissibilities are extracted. Then the conservative fine-scale total-velocity field is reconstructed by solving a local flow problem in each coarse cell. In this paper we extend the MSFV method to account for gravity effects, which enables our method to work for fairly realistic problems, e.g. dead-oil problems or black-oil problems. To correctly account for gravity effects an additional local problem has to be solved on each block of the dual grid. This problem provides an additional basis function (gravity basis function) that represents a local correction to the fluxes computed in the absence of gravity.

Adsorption III. Nonequilibrium adsorption of surfactants onto reservoir cores from the North Sea. The effects of oil and clay minerals

The adsorption of 14CO and 14CO2 on a hydrogen-reduced Cu/ZnO/Al2O3, a Cu/Al2O3 and a ZnO catalyst at 293 K is reported. With each adsorbate evidence for both a strongly and a weakly absorbed state has been detected on the copper component of the catalyst. Both a relatively rapid and a very slow adsorption of CO2 on each of the adsorbates have been detected. Adsorption of CO in the presence of preadsorbed CO2 and vice versa shows that the presence of one gas does not completely prevent the adsorption of the other. The adsorptive capacity of the Cu/ZnO/Al2O3 for CO is approximately twice that for CO2, although a larger fraction of the latter is strongly adsorbed and will displace some preadsorbed CO from the copper surface. Evidence for the dissociative adsorption of some of the CO2 to COads and surface oxygen, as well as the formation of surface carbonate by reaction of CO2 with catalyst oxygen, has been obtained. It is proposed that this latter process is responsible for the very slow CO2 adsorption process. Whilst CO2 is adsorbed on each of the components of the Cu/ZnO/Al2O3 catalyst, adsorption of CO is severely limited on the zinc oxide component and does not occur on the alumina. The results are interpreted in terms of a model in which at least three types of adsorption site exist on the copper surface. The role of residual oxygen on the surface, following hydrogen reduction, in the adsorption of CO2 is also discussed.

We have measured the H i power spectrum of the nearly face-on spiral galaxy NGC 1058 from radio-interferometric observations using a visibility based estimator. The power spectrum is well fitted by two different power laws P(U) =AUα, one with α=−2.5 ± 0.6 at small length-scales (600 pc to 1.5 kpc) and another with α=−1.0 ± 0.2 at large length-scales (1.5–10.0 kpc). We interpret this change in the slope of the power spectrum as a transition from 3D turbulence at small length-scales to 2D turbulence in the plane of the galaxy's disc at large length-scales. We use the observed break in the power spectrum to estimate the galaxy's scaleheight, which we find to be 490 ± 90 pc.

Summary Multiscale methods have been developed as a robust alternative to upscaling and to accelerate reservoir simulation. In their basic setup, multiscale methods use both a restriction operator to construct a reduced system of flow equations that can be solved on a coarser grid and a prolongation operator to map pressure unknowns from the coarse grid back to the original simulation grid. When combined with a local smoother, this gives an iterative solver that can efficiently compute approximate pressures to within a prescribed accuracy and still provide mass-conservative fluxes. We present an adaptive and flexible framework for combining multiple sets of such multiscale approximations. Each multiscale approximation can target a certain scale; geological features such as faults, fractures, facies, or other geobodies; or a particular computational challenge such as propagating displacement and chemical fronts, wells being turned on or off, and others. Multiscale methods that fit the framework are characterized by three features. First, the prolongation and restriction operators are constructed by use of a nonoverlapping partition of the fine grid. Second, the prolongation operator is composed of a set of basis functions, each of which has compact support within a support region that contains a coarse gridblock. Finally, the basis functions form a partition of unity. These assumptions are quite general and encompass almost all existing multiscale (finite-volume) methods that rely on localized basis functions. The novelty of our framework is that it enables multiple pairs of prolongation and restriction operators—computed on different coarse grids and possibly also by different basis-function formulations—to be combined into one iterative procedure. Through a series of numerical examples consisting of both idealized geology and flow physics as well as a geological model of a real asset, we demonstrate that the new iterative framework increases the accuracy and efficiency of the multiscale technology by improving the rate at which one converges the fine-scale residuals toward machine precision. In particular, we demonstrate how it is possible to combine multiscale prolongation operators that have different spatial resolution and that each individual operator can be designed to target, among others, challenging grids, including faults, pinchouts, and inactive cells; high-contrast fluvial sands; fractured carbonate reservoirs; and complex wells.

In the context of Landau theory and its field theoretical refinements, interfaces between coexisting phases are described by intrinsic profiles. These intrinsic interface profiles, however, are neither directly accessible by experiment nor by computer simulation as they are broadened by long-wavelength capillary waves. In this paper we study the separation of the small scale intrinsic structure from the large scale capillary wave fluctuations in the Monte Carlo simulated three-dimensional Ising model. To this purpose, a blocking procedure is applied, using the block size as a variable cutoff, and a translationally invariant method to determine the interface position of strongly fluctuating profiles on small length scales is introduced. While the capillary wave picture is confirmed on large length scales and its limit of validity is estimated, an intrinsic regime is, contrary to expectations, not observed.

Metallic multilayers can be used as ultra-high strength coatings. They exhibit a very strong Hall–Petch-like size-effect where the mechanical strength depends on the layer thickness. This trend suggests that dislocation pileup theory can be used to predict the strength of multilayers from fundamental and microscopic material parameters. At large length scales, the behavior of multilayers can be described by a scaling law. At small length scales, the effect of discrete dislocations becomes important, and large deviation from the scaling law occurs. A complete analytic model should apply at all length scales and properly account for this dislocation discreteness effect. Such a model is proposed here. The layer thickness of multilayers are divided into four length-scale regimes, and simple analytic formulas are given for both the regime length scales and multilayer strength in each regime. The model is applied to Cu/Ni multilayers and the predicted strength is compared to experimental data. Furthermore, the predicted polycrystalline multilayer deformation map is presented.

An analytically tractable model for chain molecules with bending stiffness is presented and the dynamical properties of such chains are investigated. The partition function is derived via the maximum entropy principle taking into account the chain connectivity as well as the bending restrictions in form of constraints. We demonstrate that second moments agree exactly with those known from the Kratky‐Porod wormlike chain. Moreover, various distribution functions are calculated. In particular, the static structure factor is shown to be proportional to 1/q at large scattering vectors q. The equations of motion for a chain in a melt as well as in dilute solution are presented. In the latter case the hydrodynamic interaction is taken into account via the Rotne‐Prager tensor. The dynamical equations are solved by a normal mode analysis. In the limit of a flexible chain the model reproduces the well‐known Rouse and Zimm dynamics, respectively, on large length scales, whereas in the rod limit the eigenfunctions correspond to bending motion only. In addition, the coherent and incoherent dynamic structure factor is discussed. For melts we show that at large scattering vectors the incoherent dynamic structure factor is a universal function of only the combination q8/3tp1/3, where 1/(2p) is the persistence length of the macromolecules. The comparison of the theoretical results with quasielastic neutron and light scattering experiments of various polymers in solution and melt exhibits good agreement. Our investigations show that local stiffness strongly influences the dynamics of macromolecules on small length scales even for long and flexible chains.

Understanding molecular conformation is a first step in understanding the waxing (or formation of crystals) of petroleum fuels. In this work, we study the molecular conformation of typical fuel oils modeled as pure n-alkanes. A multi-scale global optimization methodology based on terrain methods and funneling algorithms is used to find minimum energy molecular conformations of united atom n-alkane models for diesel, home heating, and residual fuel oils. The terrain method is used to gather average gradient and average Hessian matrix information at the small length scale while funneling is used to generate conformational changes at the large length scale that drive iterates to a global minimum on the potential energy surface. In addition, the funneling method uses a mixture of average and point-wise derivative information to produce a monotonically decreasing sequence of objective function values and to avoid getting trapped at local minima on the potential energy surface. Computational results clearly show that the calculated united atom molecular conformations are comprised of zigzag structure with considerable wrapping at the ends of the molecule and that planar zigzag conformations usually correspond to saddle points. Furthermore, the numerical results clearly demonstrate that our terrain/funneling approach is robust and fast.